Elliptic curve isogeny class with LMFDB label 481650.gq (Cremona label 481650gq)

• Label: 481650.gq
• Number of curves: $4$
• Conductor: $481650$
• CM: no
• Rank: $1$

Elliptic curves in class 481650.gq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
481650.gq1	481650gq3	\([1, 1, 1, -12844088, 17712172031]\)	\(3107086841064961/570\)	\(42988767656250\)	\([2]\)	\(21233664\)	\(2.4517\)	\(\Gamma_0(N)\)-optimal^*
481650.gq2	481650gq4	\([1, 1, 1, -929588, 183154031]\)	\(1177918188481/488703750\)	\(36857494669277343750\)	\([2]\)	\(21233664\)	\(2.4517\)
481650.gq3	481650gq2	\([1, 1, 1, -802838, 276442031]\)	\(758800078561/324900\)	\(24503597564062500\)	\([2, 2]\)	\(10616832\)	\(2.1051\)	\(\Gamma_0(N)\)-optimal^*
481650.gq4	481650gq1	\([1, 1, 1, -42338, 5704031]\)	\(-111284641/123120\)	\(-9285573813750000\)	\([2]\)	\(5308416\)	\(1.7586\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 481650.gq1.

Rank

The elliptic curves in class 481650.gq have rank \(1\).

Complex multiplication

The elliptic curves in class 481650.gq do not have complex multiplication.

Modular form 481650.2.a.gq

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.