Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-28672.7-t
Conductor 28672.7
Rank \( 1 \)

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

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

Curve label Weierstrass Coefficients
28672.7-t1 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 853 a + 169\) , \( 809 a + 16525\bigr] \)
28672.7-t2 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -159 a + 101\) , \( 491 a - 1289\bigr] \)
28672.7-t3 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 53 a + 9\) , \( 9 a + 237\bigr] \)
28672.7-t4 \( \bigl[0\) , \( -a\) , \( 0\) , \( -5 a - 50\) , \( -41 a - 106\bigr] \)
28672.7-t5 \( \bigl[0\) , \( a\) , \( 0\) , \( -21 a - 2\) , \( 105 a - 54\bigr] \)
28672.7-t6 \( \bigl[0\) , \( -a\) , \( 0\) , \( -85 a + 190\) , \( -169 a - 1130\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph