Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-25600.7-c
Conductor 25600.7
Rank \( 0 \)

Related objects

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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 25600.7-c over \(\Q(\sqrt{-7}) \)

Isogeny class 25600.7-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
25600.7-c1 \( \bigl[0\) , \( 0\) , \( 0\) , \( -13 a - 13\) , \( -34 a + 102\bigr] \)
25600.7-c2 \( \bigl[0\) , \( 0\) , \( 0\) , \( 7 a + 7\) , \( -6 a + 18\bigr] \)
25600.7-c3 \( \bigl[0\) , \( 0\) , \( 0\) , \( 2 a + 2\) , \( a - 3\bigr] \)
25600.7-c4 \( \bigl[0\) , \( 0\) , \( 0\) , \( 107 a + 107\) , \( -426 a + 1278\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph