Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-28672.9-l
Conductor 28672.9
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 28672.9-l over \(\Q(\sqrt{-7}) \)

Isogeny class 28672.9-l contains 4 curves linked by isogenies of degrees dividing 10.

Curve label Weierstrass Coefficients
28672.9-l1 \( \bigl[0\) , \( 1\) , \( 0\) , \( -19 a + 26\) , \( -3 a + 70\bigr] \)
28672.9-l2 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -240 a + 88\) , \( 988 a - 2452\bigr] \)
28672.9-l3 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 8\) , \( -4 a + 12\bigr] \)
28672.9-l4 \( \bigl[0\) , \( 1\) , \( 0\) , \( 221 a - 534\) , \( -2723 a + 3878\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 10 & 2 & 5 \\ 10 & 1 & 5 & 2 \\ 2 & 5 & 1 & 10 \\ 5 & 2 & 10 & 1 \end{array}\right)\)

Isogeny graph