Elliptic curve isogeny class with LMFDB label 1216.e (Cremona label 1216b)

• Label: 1216.e
• Number of curves: $3$
• Conductor: $1216$
• CM: no
• Rank: $1$

Elliptic curves in class 1216.e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1216.e1	1216b3	$[0, -1, 0, -5473, -1251871]$	$-69173457625/2550136832$	$-668503069687808$	$[]$	$3456$	$1.5249$
1216.e2	1216b1	$[0, -1, 0, -993, 12385]$	$-413493625/152$	$-39845888$	$[]$	$384$	$0.42628$	$\Gamma_0(N)$-optimal
1216.e3	1216b2	$[0, -1, 0, 607, 45601]$	$94196375/3511808$	$-920599396352$	$[]$	$1152$	$0.97558$

Rank

The elliptic curves in class 1216.e have rank $1$.

Complex multiplication

The elliptic curves in class 1216.e do not have complex multiplication.

Modular form 1216.2.a.e

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.