Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-28672.7-h
Conductor 28672.7
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 28672.7-h over \(\Q(\sqrt{-7}) \)

Isogeny class 28672.7-h contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
28672.7-h1 \( \bigl[0\) , \( a\) , \( 0\) , \( -853 a + 1022\) , \( 809 a - 17334\bigr] \)
28672.7-h2 \( \bigl[0\) , \( -a\) , \( 0\) , \( 159 a - 58\) , \( 491 a + 798\bigr] \)
28672.7-h3 \( \bigl[0\) , \( a\) , \( 0\) , \( -53 a + 62\) , \( 9 a - 246\bigr] \)
28672.7-h4 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 85 a + 105\) , \( -169 a + 1299\bigr] \)
28672.7-h5 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 21 a - 23\) , \( 105 a - 51\bigr] \)
28672.7-h6 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 5 a - 55\) , \( -41 a + 147\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 8 & 4 & 4 \\ 8 & 1 & 4 & 4 & 8 & 2 \\ 2 & 4 & 1 & 4 & 2 & 2 \\ 8 & 4 & 4 & 1 & 8 & 2 \\ 4 & 8 & 2 & 8 & 1 & 4 \\ 4 & 2 & 2 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph