Elliptic curve isogeny class 432.1-k over number field Q(7)\Q(\sqrt{7})

• Base field: $\Q(\sqrt{7})$
• Label: 2.2.28.1-432.1-k
• Conductor: 432.1
• Rank: $0$

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

Generator $a$, with minimal polynomial $x^{2} - 7$; class number $1$.

Rank

Rank: $0$

Isogeny matrix

$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$

Isogeny graph

Elliptic curves in class 432.1-k over $\Q(\sqrt{7})$

Isogeny class 432.1-k contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
432.1-k1	$\bigl[a + 1$ , $-a - 1$ , $a + 1$ , $27 a - 78$ , $430 a - 1141\bigr]$
432.1-k2	$\bigl[a + 1$ , $-a - 1$ , $a + 1$ , $677 a - 1798$ , $16142 a - 42711\bigr]$
432.1-k3	$\bigl[a + 1$ , $-a - 1$ , $a + 1$ , $907 a - 2408$ , $4796 a - 12693\bigr]$
432.1-k4	$\bigl[a + 1$ , $-a - 1$ , $a + 1$ , $10847 a - 28708$ , $1008896 a - 2669289\bigr]$