Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-121.2-a
Conductor 121.2
Rank \( 1 \)

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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 121.2-a over \(\Q(\sqrt{-7}) \)

Isogeny class 121.2-a contains 3 curves linked by isogenies of degrees dividing 25.

Curve label Weierstrass Coefficients
121.2-a1 \( \bigl[0\) , \( -1\) , \( 1\) , \( -7820\) , \( -263580\bigr] \)
121.2-a2 \( \bigl[0\) , \( -1\) , \( 1\) , \( -10\) , \( -20\bigr] \)
121.2-a3 \( \bigl[0\) , \( -1\) , \( 1\) , \( 0\) , \( 0\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph