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mordell
† ˈmordell Obs. [app. repr. an OE. type *morᵹendǽl, f. morᵹen morn, morrow + dǽl deal n.1 Cf. the synonymous morrow-part.] The share of the husband's property to which a widow was entitled, as representing her ‘morning-gift’.1552 Will of Baldwin (Somerset Ho.), [Mentions his wife's] mordell [part of...
Oxford English Dictionary
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Bob Mordell
Mordell went on the 1979 tour of Japan with England but did not feature in the test matches. Mordell signed for Kent Invicta before their début season in 1983 for £13,500.
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Mordell–Weil group
It is simply the group of -points of , so is the Mordell–Weil grouppg 207. See also
Mordell–Weil theorem
References
Further examples and cases
The Mordell–Weil Group of Curves of Genus 2
Determining the Mordell–Weil group
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Find all positive integers that solve Mordell's equation $y^2=x^3+37$ Find all Mordell's equation: $$y^2=x^3+k$$ where $k=37$ positive integer numbers,I can't find the when $k=37$ the mordell equation solution with s...
If there exists $a$ such as $k=3a^2\pm1$ then the only solutions to the Mordell equation are $(a^2+k,\pm a(a^2-3k))$. See this paper for more details : Paper on Mordell's equation and another one.
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Louis J. Mordell
His basic work on Mordell's theorem is from 1921 to 1922, as is the formulation of the Mordell conjecture. Mordell is said to have hated administrative duties.
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About Mordell's Theorem (Elliptic Curves) I've just finished the proof of Mordell's Theorem given in the book "Rational Points on Elliptic Curves " by Silverman. One of the key lemmas used in the proof of the theore...
The proof of that result, usually called (an explicit version of) the Weak Mordell-Weil theorem, can be found in Silverman's _Arithmetic of Elliptic Curves
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Mordell curve
Properties
If (x, y) is an integer point on a Mordell curve, then so is (x, -y). Gebel, Data on Mordell's curves for –10000 ≤ n ≤ 10000
M.
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Is there an analogue of Mordell-Weil theorem for other fields? The Mordell-Weil theorem states that for an abelian variety $A$ over a **number field** $K$ the group of $K$-rational points of $A$ is finitely generated ...
For $K=\Bbb Q_p$ there will be uncountably many $K$-rational points. The exact structure of $K$-rational points will depend on the reduction type of the curve, but points close to the base-point $O$ are in essence parameterised by the formal group of the curve. See Silverman's book for much more det...
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Mordell–Weil theorem
abelian group, called the Mordell–Weil group. 1901; it was proved by Louis Mordell in 1922.
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Variation of Mordell's equation Determine all integral solutions to the equation $$3x^2+4=y^3$$ I'm not even sure where to start with this.
Hint : Considering in mod $3$ helps. > We have to have $y\equiv 1\pmod 3$. Let $y=3k+1$ where $k\in\mathbb Z$. Then, the equation can be written as $x^2=3(3k^3+3k^2+k)-1$. So $x^2\equiv 2\pmod 3$, which is impossible.
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Chowla–Mordell theorem
It was proved and published independently by Sarvadaman Chowla and Louis Mordell, around 1951. The 'if' part was known to Gauss: the contribution of Chowla and Mordell was the 'only if' direction.
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Solving the Mordell equation $y^2 = x^3 − 2$; what would be a general strategy? I am looking at the solution provided in my lecture notes for solving this particular Mordell equation: $$y^2 = x^3 − 2$$ which factors...
If something divides $a$ and $b$, it divides $a-b$. So a common factor of $y+\sqrt{-2}$ and $y-\sqrt{-2}$ divides $(y+\sqrt{-2}) - (y-\sqrt{-2}) = 2\sqrt{-2}$.
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Erdős–Mordell inequality
It is named after Paul Erdős and Louis Mordell. posed the problem of proving the inequality; a proof was provided two years later by . External links
Alexander Bogomolny, "Erdös-Mordell Inequality", from Cut-the-Knot.
Triangle inequalities
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Elliptic curves with trivial Mordell–Weil group over certain fields. I am looking for elliptic curves $E,E'$ defined over $\mathbb{F}_{3}$ and $\mathbb{F}_{4}$ respectively and given by a Weierstrass equation such tha...
By Hasse's bound we know that $1\le |E(\mathbb{F}_3)|\le 7$; and indeed there is an elliptic curve with $E(\mathbb{F}_{3})=\\{\mathcal{O}\\}$, given by $$ y^2=x^3-x-1. $$ Actually, since we know that all such curves are given by the long Weierstrass equation $y^2=x^3+ax^2+bx+c$ with nonzero discrimi...
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When does a Mordell curve have non-trivial torsion? Is there a known simple criteria for when a Mordell curve has non-trivial torsion? A comment in this question: Family of elliptic curves with trivial torsion Sugg...
Here is a further reference, extending the result you have linked. **Theorem:** If $k$ is square-free and not equal to $1$, the elliptic curve $y^2 = x^3+k$ has no rational torsion points. _Proof:_ See A. Knapp, Elliptic Curves, Princeton Univ. Press, 1992, Theorem $5.3$. More generally, there is in...
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