Elliptic curve isogeny class 36.2-c over number field Q(157)\Q(\sqrt{157})

• Base field: $\Q(\sqrt{157})$
• Label: 2.2.157.1-36.2-c
• Conductor: 36.2
• Rank: $2$

Base field $\Q(\sqrt{157})$

Generator $a$, with minimal polynomial $x^{2} - x - 39$; class number $1$.

Elliptic curves in class 36.2-c over $\Q(\sqrt{157})$

Isogeny class 36.2-c contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
36.2-c1	$\bigl[a + 1$ , $-a - 1$ , $a + 1$ , $1900584 a - 12857429$ , $-3563273659 a + 24105482317\bigr]$
36.2-c2	$\bigl[a + 1$ , $-a - 1$ , $a + 1$ , $7069 a - 47834$ , $512606 a - 3467771\bigr]$

Rank

Rank: $2$

Isogeny matrix

$\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)$

Isogeny graph