Elliptic curve isogeny class 28672.7-k over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-28672.7-k
• Conductor: 28672.7
• Rank: \( 0 \)

Base field \(\Q(\sqrt{-7}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x + 2 \); class number \(1\).

Elliptic curves in class 28672.7-k over \(\Q(\sqrt{-7}) \)

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

Curve label	Weierstrass Coefficients
28672.7-k1	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 853 a + 169\) , \( -809 a - 16525\bigr] \)
28672.7-k2	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -159 a + 101\) , \( -491 a + 1289\bigr] \)
28672.7-k3	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 53 a + 9\) , \( -9 a - 237\bigr] \)
28672.7-k4	\( \bigl[0\) , \( a\) , \( 0\) , \( -5 a - 50\) , \( 41 a + 106\bigr] \)
28672.7-k5	\( \bigl[0\) , \( -a\) , \( 0\) , \( -21 a - 2\) , \( -105 a + 54\bigr] \)
28672.7-k6	\( \bigl[0\) , \( a\) , \( 0\) , \( -85 a + 190\) , \( 169 a + 1130\bigr] \)

Rank

Rank: \( 0 \)

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