Elliptic curve isogeny class 288.1-c over number field Q(3)\Q(\sqrt{3})

• Base field: $\Q(\sqrt{3})$
• Label: 2.2.12.1-288.1-c
• Conductor: 288.1
• Rank: $1$

Base field $\Q(\sqrt{3})$

Generator $a$, with minimal polynomial $x^{2} - 3$; class number $1$.

Elliptic curves in class 288.1-c over $\Q(\sqrt{3})$

Isogeny class 288.1-c contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
288.1-c1	$\bigl[0$ , $a$ , $0$ , $4063804 a - 7038714$ , $5839863922 a - 10114941022\bigr]$
288.1-c2	$\bigl[a + 1$ , $-a - 1$ , $0$ , $381758 a - 661224$ , $-168866036 a + 292484554\bigr]$
288.1-c3	$\bigl[a + 1$ , $-a - 1$ , $0$ , $23873 a - 41349$ , $-2630312 a + 4555834\bigr]$
288.1-c4	$\bigl[0$ , $a$ , $0$ , $113682 a - 196902$ , $-3469554 a + 6009444\bigr]$
288.1-c5	$\bigl[a + 1$ , $-a - 1$ , $a + 1$ , $77 a - 140$ , $-1664 a + 2879\bigr]$
288.1-c6	$\bigl[a + 1$ , $-a - 1$ , $0$ , $-1569806 a + 2718984$ , $-176681708 a + 306021695\bigr]$

Rank

Rank: $1$

Isogeny matrix

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

Isogeny graph