Elliptic curve isogeny class with Cremona label 458640gp (LMFDB label 458640.gp)

• Label: 458640gp
• Number of curves: $4$
• Conductor: $458640$
• CM: no
• Rank: $0$

Elliptic curves in class 458640gp

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
458640.gp4	458640gp1	\([0, 0, 0, 4290342, -3717725893]\)	\(6364491337435136/8034291412875\)	\(-11025120151454371326000\)	\([2]\)	\(35389440\)	\(2.9156\)	\(\Gamma_0(N)\)-optimal^*
458640.gp3	458640gp2	\([0, 0, 0, -25893903, -35960536402]\)	\(87450143958975184/25164018140625\)	\(552504377521929924000000\)	\([2, 2]\)	\(70778880\)	\(3.2621\)	\(\Gamma_0(N)\)-optimal^*
458640.gp2	458640gp3	\([0, 0, 0, -154886403, 713666478098]\)	\(4678944235881273796/202428825314625\)	\(17778211968841718599296000\)	\([2]\)	\(141557760\)	\(3.6087\)	\(\Gamma_0(N)\)-optimal^*
458640.gp1	458640gp4	\([0, 0, 0, -379849323, -2849127423478]\)	\(69014771940559650916/9797607421875\)	\(860470050462750000000000\)	\([2]\)	\(141557760\)	\(3.6087\)

^*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 458640gp1.

Rank

The elliptic curves in class 458640gp have rank \(0\).

Complex multiplication

The elliptic curves in class 458640gp do not have complex multiplication.

Modular form 458640.2.a.gp

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.