Elliptic curve isogeny class with Cremona label 482664cq (LMFDB label 482664.cq)

• Label: 482664cq
• Number of curves: $4$
• Conductor: $482664$
• CM: no
• Rank: $0$

Elliptic curves in class 482664cq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
482664.cq4	482664cq1	\([0, 1, 0, -119422892, 506946160800]\)	\(-152435594466395827792/1646846627220711\)	\(-2034947615203474647346944\)	\([2]\)	\(79626240\)	\(3.4803\)	\(\Gamma_0(N)\)-optimal^*
482664.cq3	482664cq2	\([0, 1, 0, -1915693472, 32272195097520]\)	\(157304700372188331121828/18069292138401\)	\(89310230443277509026816\)	\([2, 2]\)	\(159252480\)	\(3.8269\)	\(\Gamma_0(N)\)-optimal^*
482664.cq1	482664cq3	\([0, 1, 0, -30651094712, 2065451256913968]\)	\(322159999717985454060440834/4250799\)	\(42020443894560768\)	\([2]\)	\(318504960\)	\(4.1735\)	\(\Gamma_0(N)\)-optimal^*
482664.cq2	482664cq4	\([0, 1, 0, -1920621512, 32097805560432]\)	\(79260902459030376659234/842751810121431609\)	\(8330858540770134391205234688\)	\([2]\)	\(318504960\)	\(4.1735\)

^*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 482664cq1.

Rank

The elliptic curves in class 482664cq have rank \(0\).

Complex multiplication

The elliptic curves in class 482664cq do not have complex multiplication.

Modular form 482664.2.a.cq

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.