Properties

Base field \(\Q(\sqrt{7}) \)
Label 2.2.28.1-256.1-a
Conductor 256.1
Rank not recorded

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

Generator \(a\), with minimal polynomial \( x^{2} - 7 \); class number \(1\).

Elliptic curves in class 256.1-a over \(\Q(\sqrt{7}) \)

Isogeny class 256.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
256.1-a1 \( \bigl[0\) , \( -1\) , \( 0\) , \( -4 a - 10\) , \( -6 a - 16\bigr] \)
256.1-a2 \( \bigl[0\) , \( -1\) , \( 0\) , \( 4 a - 10\) , \( 6 a - 16\bigr] \)
256.1-a3 \( \bigl[0\) , \( -1\) , \( 0\) , \( 64 a - 170\) , \( 434 a - 1148\bigr] \)
256.1-a4 \( \bigl[0\) , \( -1\) , \( 0\) , \( -64 a - 170\) , \( -434 a - 1148\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph