Elliptic curve isogeny class 64.3-b over number field Q(33)\Q(\sqrt{33})

• Base field: $\Q(\sqrt{33})$
• Label: 2.2.33.1-64.3-b
• Conductor: 64.3
• Rank: $0$

Base field $\Q(\sqrt{33})$

Generator $a$, with minimal polynomial $x^{2} - x - 8$; class number $1$.

Elliptic curves in class 64.3-b over $\Q(\sqrt{33})$

Isogeny class 64.3-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
64.3-b1	$\bigl[0$ , $-a - 1$ , $0$ , $a + 3$ , $-11 a + 34\bigr]$
64.3-b2	$\bigl[0$ , $-a - 1$ , $0$ , $a + 3$ , $-11 a - 26\bigr]$
64.3-b3	$\bigl[0$ , $-a - 1$ , $0$ , $41 a - 132$ , $-212 a + 712\bigr]$
64.3-b4	$\bigl[0$ , $-a - 1$ , $0$ , $-39 a - 92$ , $-172 a - 408\bigr]$

Rank

Rank: $0$

Isogeny matrix

$\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)$

Isogeny graph