Elliptic curve isogeny class 169.1-b over number field Q(3)\Q(\sqrt{3})

• Base field: $\Q(\sqrt{3})$
• Label: 2.2.12.1-169.1-b
• Conductor: 169.1
• Rank: $0$

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

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

Elliptic curves in class 169.1-b over $\Q(\sqrt{3})$

Isogeny class 169.1-b contains 6 curves linked by isogenies of degrees dividing 18.

Curve label	Weierstrass Coefficients
169.1-b1	$\bigl[a + 1$ , $a$ , $a$ , $957 a - 1656$ , $20670 a - 35801\bigr]$
169.1-b2	$\bigl[a + 1$ , $0$ , $a$ , $11 a - 21$ , $-27 a + 46\bigr]$
169.1-b3	$\bigl[a + 1$ , $0$ , $a$ , $16 a - 46$ , $16 a - 66\bigr]$
169.1-b4	$\bigl[a + 1$ , $a$ , $a$ , $42 a - 71$ , $-182 a + 316\bigr]$
169.1-b5	$\bigl[a + 1$ , $a$ , $a$ , $77462 a - 134191$ , $15405299 a - 26682837\bigr]$
169.1-b6	$\bigl[a + 1$ , $0$ , $a$ , $991 a - 3101$ , $31242 a - 74777\bigr]$

Rank

Rank: $0$

Isogeny matrix

$\left(\begin{array}{rrrrrr} 1 & 6 & 2 & 3 & 3 & 6 \\ 6 & 1 & 3 & 2 & 18 & 9 \\ 2 & 3 & 1 & 6 & 6 & 3 \\ 3 & 2 & 6 & 1 & 9 & 18 \\ 3 & 18 & 6 & 9 & 1 & 2 \\ 6 & 9 & 3 & 18 & 2 & 1 \end{array}\right)$

Isogeny graph