Elliptic curve isogeny class 150.1-b over number field Q(6)\Q(\sqrt{6})

• Base field: $\Q(\sqrt{6})$
• Label: 2.2.24.1-150.1-b
• Conductor: 150.1
• Rank: $0$

Base field $\Q(\sqrt{6})$

Generator $a$, with minimal polynomial $x^{2} - 6$; class number $1$.

Elliptic curves in class 150.1-b over $\Q(\sqrt{6})$

Isogeny class 150.1-b contains 12 curves linked by isogenies of degrees dividing 24.

Curve label	Weierstrass Coefficients
150.1-b1	$\bigl[a + 1$ , $-a$ , $0$ , $-5606 a - 13776$ , $-395577 a - 969132\bigr]$
150.1-b2	$\bigl[a + 1$ , $0$ , $0$ , $271 a - 661$ , $-12352 a + 30257\bigr]$
150.1-b3	$\bigl[a + 1$ , $0$ , $0$ , $-29 a + 74$ , $416 a - 1018\bigr]$
150.1-b4	$\bigl[a + 1$ , $-a$ , $0$ , $35919 a + 87939$ , $803878 a + 1968921\bigr]$
150.1-b5	$\bigl[a + 1$ , $-a$ , $0$ , $-9071 a - 22221$ , $98592 a + 241497\bigr]$
150.1-b6	$\bigl[a + 1$ , $0$ , $0$ , $1371 a - 3356$ , $-36992 a + 90612\bigr]$
150.1-b7	$\bigl[a + 1$ , $-a$ , $0$ , $-371 a - 906$ , $-5568 a - 13638\bigr]$
150.1-b8	$\bigl[a + 1$ , $0$ , $0$ , $-35919 a + 87939$ , $-803878 a + 1968921\bigr]$
150.1-b9	$\bigl[a + 1$ , $-a$ , $0$ , $-6671 a - 16341$ , $462144 a + 1132017\bigr]$
150.1-b10	$\bigl[a + 1$ , $-a$ , $0$ , $-5771 a - 14136$ , $-374496 a - 917328\bigr]$
150.1-b11	$\bigl[a + 1$ , $-a$ , $0$ , $-106671 a - 261341$ , $29666144 a + 72667017\bigr]$
150.1-b12	$\bigl[a + 1$ , $0$ , $0$ , $5606 a - 13776$ , $395577 a - 969132\bigr]$

Rank

Rank: $0$

Isogeny matrix

$\left(\begin{array}{rrrrrrrrrrrr} 1 & 24 & 8 & 3 & 6 & 8 & 4 & 12 & 12 & 2 & 24 & 4 \\ 24 & 1 & 3 & 8 & 4 & 12 & 6 & 8 & 2 & 12 & 4 & 24 \\ 8 & 3 & 1 & 24 & 12 & 4 & 2 & 24 & 6 & 4 & 12 & 8 \\ 3 & 8 & 24 & 1 & 2 & 24 & 12 & 4 & 4 & 6 & 8 & 12 \\ 6 & 4 & 12 & 2 & 1 & 12 & 6 & 2 & 2 & 3 & 4 & 6 \\ 8 & 12 & 4 & 24 & 12 & 1 & 2 & 24 & 6 & 4 & 3 & 8 \\ 4 & 6 & 2 & 12 & 6 & 2 & 1 & 12 & 3 & 2 & 6 & 4 \\ 12 & 8 & 24 & 4 & 2 & 24 & 12 & 1 & 4 & 6 & 8 & 3 \\ 12 & 2 & 6 & 4 & 2 & 6 & 3 & 4 & 1 & 6 & 2 & 12 \\ 2 & 12 & 4 & 6 & 3 & 4 & 2 & 6 & 6 & 1 & 12 & 2 \\ 24 & 4 & 12 & 8 & 4 & 3 & 6 & 8 & 2 & 12 & 1 & 24 \\ 4 & 24 & 8 & 12 & 6 & 8 & 4 & 3 & 12 & 2 & 24 & 1 \end{array}\right)$

Isogeny graph