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searching for Mordell–Weil group 7 found (18 total)

Steven Zucker (345 words) [view diff] exact match in snippet view article find links to article

a given set of sections provides a basis (up to torsion) for the Mordell–Weil group of an elliptic surface E → S {\displaystyle E\to S} , where S {\displaystyle

Rank of an elliptic curve (2,795 words) [view diff] exact match in snippet view article find links to article

the Mordell-Weil group of an elliptic curve E / Q {\displaystyle E/\mathbb {Q} } . Denote by E ( Q ) {\displaystyle E(\mathbb {Q} )} the Mordell-Weil group

Fermat curve (355 words) [view diff] case mismatch in snippet view article find links to article

Gross, Benedict H.; Rohrlich, David E. (1978), "Some Results on the Mordell-Weil Group of the Jacobian of the Fermat Curve" (PDF), Inventiones Mathematicae

Kummer theory (1,970 words) [view diff] exact match in snippet view article find links to article

{} H^{1}(L,E)[m]\xrightarrow {} 0} . The computation of the weak Mordell-Weil group E ( L ) / m E ( L ) {\displaystyle E(L)/mE(L)} is a key part of the

Elliptic surface (1,883 words) [view diff] exact match in snippet view article find links to article

group structure of the singular fibers is useful for computing the Mordell-Weil group of an elliptic fibration (the group of sections), in particular its

Rational point (3,028 words) [view diff] exact match in snippet view article find links to article

is finitely generated. Computer algebra programs can determine the Mordell–Weil group X(k) in many examples, but it is not known whether there is an algorithm

Birch and Swinnerton-Dyer conjecture (3,132 words) [view diff] exact match in snippet view article find links to article

1. Bhargava & Shankar (2015) proved that the average rank of the Mordell–Weil group of an elliptic curve over Q is bounded above by 7/6. Combining this