Elliptic curve isogeny class 441.1-a over number field Q(7)\Q(\sqrt{7})

• Base field: $\Q(\sqrt{7})$
• Label: 2.2.28.1-441.1-a
• Conductor: 441.1
• Rank: $0$

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

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

Elliptic curves in class 441.1-a over $\Q(\sqrt{7})$

Isogeny class 441.1-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
441.1-a1	$\bigl[a$ , $-a - 1$ , $1$ , $11430 a - 30242$ , $-3021358 a + 7993761\bigr]$
441.1-a2	$\bigl[1$ , $-a - 1$ , $a$ , $-4956 a - 13127$ , $2950874 a + 7807239\bigr]$
441.1-a3	$\bigl[a$ , $-a - 1$ , $1$ , $-330 a + 873$ , $-1537 a + 4066\bigr]$
441.1-a4	$\bigl[1$ , $-a - 1$ , $a$ , $-1351 a - 3572$ , $-7900 a - 20903\bigr]$
441.1-a5	$\bigl[1$ , $-a - 1$ , $a$ , $-13111 a - 34687$ , $1336023 a + 3534782\bigr]$
441.1-a6	$\bigl[a$ , $-a - 1$ , $1$ , $16470 a - 43577$ , $-1850335 a + 4895526\bigr]$
441.1-a7	$\bigl[a$ , $-a - 1$ , $1$ , $4955 a - 13127$ , $2950874 a - 7807241\bigr]$
441.1-a8	$\bigl[a$ , $-a - 1$ , $1$ , $263430 a - 696992$ , $-119416672 a + 315946791\bigr]$

Rank

Rank: $0$

Isogeny matrix

$\left(\begin{array}{rrrrrrrr} 1 & 16 & 8 & 4 & 8 & 2 & 16 & 4 \\ 16 & 1 & 8 & 4 & 2 & 8 & 4 & 16 \\ 8 & 8 & 1 & 2 & 4 & 4 & 8 & 8 \\ 4 & 4 & 2 & 1 & 2 & 2 & 4 & 4 \\ 8 & 2 & 4 & 2 & 1 & 4 & 2 & 8 \\ 2 & 8 & 4 & 2 & 4 & 1 & 8 & 2 \\ 16 & 4 & 8 & 4 & 2 & 8 & 1 & 16 \\ 4 & 16 & 8 & 4 & 8 & 2 & 16 & 1 \end{array}\right)$

Isogeny graph