Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-268.4-a
Conductor 268.4
Rank \( 0 \)

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Base field \(\Q(\sqrt{-7}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x + 2 \); class number \(1\).

Elliptic curves in class 268.4-a over \(\Q(\sqrt{-7}) \)

Isogeny class 268.4-a contains 3 curves linked by isogenies of degrees dividing 9.

Curve label Weierstrass Coefficients
268.4-a1 \( \bigl[1\) , \( 1\) , \( 0\) , \( 9 a - 5\) , \( -5 a - 5\bigr] \)
268.4-a2 \( \bigl[1\) , \( 1\) , \( 0\) , \( -a\) , \( -a\bigr] \)
268.4-a3 \( \bigl[1\) , \( 1\) , \( 0\) , \( 209 a - 60\) , \( 797 a + 1158\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 3 \\ 3 & 1 & 9 \\ 3 & 9 & 1 \end{array}\right)\)

Isogeny graph