Elliptic curve isogeny class 896.7-b over number field Q(−7)\Q(\sqrt{-7})

• Base field: $\Q(\sqrt{-7})$
• Label: 2.0.7.1-896.7-b
• Conductor: 896.7
• Rank: $0$

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

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

Elliptic curves in class 896.7-b over $\Q(\sqrt{-7})$

Isogeny class 896.7-b contains 12 curves linked by isogenies of degrees dividing 36.

Curve label	Weierstrass Coefficients
896.7-b1	$\bigl[a + 1$ , $-a + 1$ , $a + 1$ , $851 a - 1193$ , $14853 a - 9611\bigr]$
896.7-b2	$\bigl[a + 1$ , $a$ , $0$ , $-100 a + 11$ , $400 a - 335\bigr]$
896.7-b3	$\bigl[a + 1$ , $-a - 1$ , $a + 1$ , $-12 a + 144$ , $463 a - 201\bigr]$
896.7-b4	$\bigl[a + 1$ , $-a - 1$ , $a + 1$ , $-7 a + 9$ , $a - 15\bigr]$
896.7-b5	$\bigl[a + 1$ , $a$ , $0$ , $-5 a + 6$ , $3 a + 16\bigr]$
896.7-b6	$\bigl[a + 1$ , $-a + 1$ , $a + 1$ , $a - 3$ , $-5 a + 3\bigr]$
896.7-b7	$\bigl[a + 1$ , $-a + 1$ , $a + 1$ , $-24 a + 32$ , $97 a - 63\bigr]$
896.7-b8	$\bigl[a + 1$ , $a$ , $0$ , $255 a + 26$ , $2541 a - 2718\bigr]$
896.7-b9	$\bigl[a + 1$ , $-a - 1$ , $a + 1$ , $-17 a - 361$ , $2579 a - 629\bigr]$
896.7-b10	$\bigl[a + 1$ , $-a + 1$ , $a + 1$ , $176 a - 248$ , $1185 a - 767\bigr]$
896.7-b11	$\bigl[a + 1$ , $-a + 1$ , $a + 1$ , $51 a - 73$ , $-209 a + 135\bigr]$
896.7-b12	$\bigl[a + 1$ , $-a + 1$ , $a + 1$ , $13651 a - 19113$ , $937477 a - 606603\bigr]$

Rank

Rank: $0$

Isogeny matrix

$\left(\begin{array}{rrrrrrrrrrrr} 1 & 6 & 6 & 18 & 18 & 9 & 3 & 2 & 2 & 6 & 18 & 2 \\ 6 & 1 & 4 & 12 & 3 & 6 & 2 & 3 & 12 & 4 & 12 & 12 \\ 6 & 4 & 1 & 3 & 12 & 6 & 2 & 12 & 3 & 4 & 12 & 12 \\ 18 & 12 & 3 & 1 & 4 & 2 & 6 & 36 & 9 & 12 & 4 & 36 \\ 18 & 3 & 12 & 4 & 1 & 2 & 6 & 9 & 36 & 12 & 4 & 36 \\ 9 & 6 & 6 & 2 & 2 & 1 & 3 & 18 & 18 & 6 & 2 & 18 \\ 3 & 2 & 2 & 6 & 6 & 3 & 1 & 6 & 6 & 2 & 6 & 6 \\ 2 & 3 & 12 & 36 & 9 & 18 & 6 & 1 & 4 & 12 & 36 & 4 \\ 2 & 12 & 3 & 9 & 36 & 18 & 6 & 4 & 1 & 12 & 36 & 4 \\ 6 & 4 & 4 & 12 & 12 & 6 & 2 & 12 & 12 & 1 & 3 & 3 \\ 18 & 12 & 12 & 4 & 4 & 2 & 6 & 36 & 36 & 3 & 1 & 9 \\ 2 & 12 & 12 & 36 & 36 & 18 & 6 & 4 & 4 & 3 & 9 & 1 \end{array}\right)$

Isogeny graph