Elliptic curve isogeny class with LMFDB label 5610.q (Cremona label 5610t)

• Label: 5610.q
• Number of curves: $8$
• Conductor: $5610$
• CM: no
• Rank: $0$

Elliptic curves in class 5610.q

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
5610.q1	5610t7	$[1, 0, 1, -201236483, -1098790303234]$	$901247067798311192691198986281/552431869440$	$552431869440$	$[2]$	$663552$	$2.9608$
5610.q2	5610t8	$[1, 0, 1, -12661763, -16927055362]$	$224494757451893010998773801/6152490825146276160000$	$6152490825146276160000$	$[2]$	$663552$	$2.9608$
5610.q3	5610t6	$[1, 0, 1, -12577283, -17169377794]$	$220031146443748723000125481/172266701724057600$	$172266701724057600$	$[2, 2]$	$331776$	$2.6142$
5610.q4	5610t4	$[1, 0, 1, -2484908, -1506795694]$	$1696892787277117093383481/1440538624914939000$	$1440538624914939000$	$[6]$	$221184$	$2.4115$
5610.q5	5610t5	$[1, 0, 1, -1627388, 790397138]$	$476646772170172569823801/5862293314453125000$	$5862293314453125000$	$[6]$	$221184$	$2.4115$
5610.q6	5610t3	$[1, 0, 1, -780803, -272099842]$	$-52643812360427830814761/1504091705903677440$	$-1504091705903677440$	$[2]$	$165888$	$2.2676$
5610.q7	5610t2	$[1, 0, 1, -189908, -12291694]$	$757443433548897303481/373234243041000000$	$373234243041000000$	$[2, 6]$	$110592$	$2.0649$
5610.q8	5610t1	$[1, 0, 1, 43372, -1467502]$	$9023321954633914439/6156756739584000$	$-6156756739584000$	$[6]$	$55296$	$1.7183$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 5610.q have rank $0$.

Complex multiplication

The elliptic curves in class 5610.q do not have complex multiplication.

Modular form 5610.2.a.q

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.

$\left(\begin{array}{rrrrrrrr} 1 & 4 & 2 & 3 & 12 & 4 & 6 & 12 \\ 4 & 1 & 2 & 12 & 3 & 4 & 6 & 12 \\ 2 & 2 & 1 & 6 & 6 & 2 & 3 & 6 \\ 3 & 12 & 6 & 1 & 4 & 12 & 2 & 4 \\ 12 & 3 & 6 & 4 & 1 & 12 & 2 & 4 \\ 4 & 4 & 2 & 12 & 12 & 1 & 6 & 3 \\ 6 & 6 & 3 & 2 & 2 & 6 & 1 & 2 \\ 12 & 12 & 6 & 4 & 4 & 3 & 2 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with LMFDB labels.