Elliptic curve isogeny class with Cremona label 425880dv (LMFDB label 425880.dv)

• Label: 425880dv
• Number of curves: $6$
• Conductor: $425880$
• CM: no
• Rank: $0$

Elliptic curves in class 425880dv

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
425880.dv4	425880dv1	\([0, 0, 0, -1118442, -455268931]\)	\(2748251600896/2205\)	\(124141279888080\)	\([2]\)	\(4718592\)	\(2.0098\)	\(\Gamma_0(N)\)-optimal^*
425880.dv3	425880dv2	\([0, 0, 0, -1126047, -448763614]\)	\(175293437776/4862025\)	\(4379704354451462400\)	\([2, 2]\)	\(9437184\)	\(2.3564\)	\(\Gamma_0(N)\)-optimal^*
425880.dv2	425880dv3	\([0, 0, 0, -2616627, 989049854]\)	\(549871953124/200930625\)	\(723991944307282560000\)	\([2, 2]\)	\(18874368\)	\(2.7030\)	\(\Gamma_0(N)\)-optimal^*
425880.dv5	425880dv4	\([0, 0, 0, 242853, -1470236794]\)	\(439608956/259416045\)	\(-934726236003374330880\)	\([2]\)	\(18874368\)	\(2.7030\)
425880.dv1	425880dv5	\([0, 0, 0, -37112907, 87002074406]\)	\(784478485879202/221484375\)	\(1596102169989600000000\)	\([2]\)	\(37748736\)	\(3.0495\)	\(\Gamma_0(N)\)-optimal^*
425880.dv6	425880dv6	\([0, 0, 0, 8030373, 6996087254]\)	\(7947184069438/7533176175\)	\(-54286984532572352870400\)	\([2]\)	\(37748736\)	\(3.0495\)

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 4 curves highlighted, and conditionally curve 425880dv1.

Rank

The elliptic curves in class 425880dv have rank \(0\).

Complex multiplication

The elliptic curves in class 425880dv do not have complex multiplication.

Modular form 425880.2.a.dv

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 Cremona numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.