Elliptic curve isogeny class 146692.2-b over number field Q(−3)\Q(\sqrt{-3})

• Base field: $\Q(\sqrt{-3})$
• Label: 2.0.3.1-146692.2-b
• Conductor: 146692.2
• Rank: $1$

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

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

Rank

Rank: $1$

Isogeny matrix

$\left(\begin{array}{rrrrr} 1 & 3 & 3 & 3 & 3 \\ 3 & 1 & 9 & 9 & 9 \\ 3 & 9 & 1 & 9 & 9 \\ 3 & 9 & 9 & 1 & 9 \\ 3 & 9 & 9 & 9 & 1 \end{array}\right)$

Isogeny graph

Elliptic curves in class 146692.2-b over $\Q(\sqrt{-3})$

Isogeny class 146692.2-b contains 5 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
146692.2-b1	$\bigl[1$ , $a - 1$ , $1$ , $54 a + 271$ , $-2763 a + 1641\bigr]$
146692.2-b2	$\bigl[1$ , $a - 1$ , $1$ , $-206 a - 2199$ , $27717 a - 3795\bigr]$
146692.2-b3	$\bigl[1$ , $a - 1$ , $1$ , $104 a - 34$ , $-183 a - 239\bigr]$
146692.2-b4	$\bigl[1$ , $a - 1$ , $1$ , $-7296 a + 3701$ , $-154103 a + 217381\bigr]$
146692.2-b5	$\bigl[1$ , $a - 1$ , $1$ , $3614 a + 24016$ , $-1825903 a + 1200467\bigr]$