Elliptic curve isogeny class 600.1-b over number field Q(3)\Q(\sqrt{3})

• Base field: $\Q(\sqrt{3})$
• Label: 2.2.12.1-600.1-b
• Conductor: 600.1
• Rank: $0$

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

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

Rank

Rank: $0$

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

Elliptic curves in class 600.1-b over $\Q(\sqrt{3})$

Isogeny class 600.1-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
600.1-b1	$\bigl[a + 1$ , $1$ , $a + 1$ , $80 a - 141$ , $-4420 a + 7659\bigr]$
600.1-b2	$\bigl[a + 1$ , $1$ , $a + 1$ , $-80 a + 139$ , $70 a - 121\bigr]$
600.1-b3	$\bigl[a + 1$ , $1$ , $a + 1$ , $20 a - 36$ , $20 a - 36\bigr]$
600.1-b4	$\bigl[a + 1$ , $1$ , $a + 1$ , $200 a - 351$ , $-1960 a + 3393\bigr]$
600.1-b5	$\bigl[0$ , $-1$ , $0$ , $-15$ , $-18\bigr]$
600.1-b6	$\bigl[a + 1$ , $1$ , $a + 1$ , $3200 a - 5601$ , $-129460 a + 224343\bigr]$