Elliptic curve isogeny class with Cremona label 462462hm (LMFDB label 462462.hm)

• Label: 462462hm
• Number of curves: $4$
• Conductor: $462462$
• CM: no
• Rank: $1$

Elliptic curves in class 462462hm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
462462.hm3	462462hm1	\([1, 1, 1, -335112, -72746871]\)	\(19968681097/628992\)	\(131096009696940288\)	\([2]\)	\(5898240\)	\(2.0594\)	\(\Gamma_0(N)\)-optimal^*
462462.hm2	462462hm2	\([1, 1, 1, -809432, 178453001]\)	\(281397674377/96589584\)	\(20131430989086392976\)	\([2, 2]\)	\(11796480\)	\(2.4060\)	\(\Gamma_0(N)\)-optimal^*
462462.hm1	462462hm3	\([1, 1, 1, -11600212, 15199218761]\)	\(828279937799497/193444524\)	\(40318168107263682636\)	\([2]\)	\(23592960\)	\(2.7525\)	\(\Gamma_0(N)\)-optimal^*
462462.hm4	462462hm4	\([1, 1, 1, 2392228, 1243965449]\)	\(7264187703863/7406095788\)	\(-1543596111302077965132\)	\([2]\)	\(23592960\)	\(2.7525\)

^*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 462462hm1.

Rank

The elliptic curves in class 462462hm have rank \(1\).

Complex multiplication

The elliptic curves in class 462462hm do not have complex multiplication.

Modular form 462462.2.a.hm

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.