Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-28672.7-m
Conductor 28672.7
Rank \( 2 \)

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-m over \(\Q(\sqrt{-7}) \)

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

Curve label Weierstrass Coefficients
28672.7-m1 \( \bigl[0\) , \( 0\) , \( 0\) , \( 12 a + 16\) , \( 24 a - 56\bigr] \)
28672.7-m2 \( \bigl[0\) , \( 0\) , \( 0\) , \( 4\) , \( -16\bigr] \)
28672.7-m3 \( \bigl[0\) , \( 0\) , \( 0\) , \( -236\) , \( 1104\bigr] \)
28672.7-m4 \( \bigl[0\) , \( 0\) , \( 0\) , \( -76\) , \( -240\bigr] \)
28672.7-m5 \( \bigl[0\) , \( 0\) , \( 0\) , \( -12 a + 28\) , \( -24 a - 32\bigr] \)
28672.7-m6 \( \bigl[0\) , \( 0\) , \( 0\) , \( -1196\) , \( -15920\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

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

Isogeny graph