Elliptic curve isogeny class with LMFDB label 162.b (Cremona label 162c)

• Label: 162.b
• Number of curves: $4$
• Conductor: $162$
• CM: no
• Rank: $0$

Elliptic curves in class 162.b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
162.b1	162c3	$[1, -1, 0, -1077, 13877]$	$-189613868625/128$	$-93312$	$[3]$	$42$	$0.26937$
162.b2	162c4	$[1, -1, 0, -852, 19664]$	$-1159088625/2097152$	$-123834728448$	$[]$	$126$	$0.81867$
162.b3	162c2	$[1, -1, 0, -42, -100]$	$-140625/8$	$-472392$	$[]$	$18$	$-0.15428$
162.b4	162c1	$[1, -1, 0, 3, -1]$	$3375/2$	$-1458$	$[3]$	$6$	$-0.70359$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 162.b have rank $0$.

Complex multiplication

The elliptic curves in class 162.b do not have complex multiplication.

Modular form 162.2.a.b

Isogeny matrix

The $i,j$ entry is the smallest degree of a cyclic isogeny between the $i$-th and $j$-th curve in the isogeny class, in the LMFDB numbering.

$\left(\begin{array}{rrrr} 1 & 3 & 21 & 7 \\ 3 & 1 & 7 & 21 \\ 21 & 7 & 1 & 3 \\ 7 & 21 & 3 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with LMFDB labels.