Elliptic curve isogeny class with Cremona label 476520cj (LMFDB label 476520.cj)

• Label: 476520cj
• Number of curves: $6$
• Conductor: $476520$
• CM: no
• Rank: $0$

Elliptic curves in class 476520cj

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
476520.cj5	476520cj1	\([0, 1, 0, -63295, -10265650]\)	\(-37256083456/38671875\)	\(-29109638868750000\)	\([2]\)	\(3538944\)	\(1.8545\)	\(\Gamma_0(N)\)-optimal^*
476520.cj4	476520cj2	\([0, 1, 0, -1191420, -500774400]\)	\(15529488955216/6125625\)	\(73775468748960000\)	\([2, 2]\)	\(7077888\)	\(2.2010\)	\(\Gamma_0(N)\)-optimal^*
476520.cj3	476520cj3	\([0, 1, 0, -1371920, -339190800]\)	\(5927735656804/2401490025\)	\(115691739073369113600\)	\([2, 2]\)	\(14155776\)	\(2.5476\)	\(\Gamma_0(N)\)-optimal^*
476520.cj1	476520cj4	\([0, 1, 0, -19060920, -32036868000]\)	\(15897679904620804/2475\)	\(119233080806400\)	\([2]\)	\(14155776\)	\(2.5476\)
476520.cj2	476520cj5	\([0, 1, 0, -10108120, 12129113840]\)	\(1185450336504002/26043266205\)	\(2509267768794627287040\)	\([2]\)	\(28311552\)	\(2.8942\)	\(\Gamma_0(N)\)-optimal^*
476520.cj6	476520cj6	\([0, 1, 0, 4476280, -2463257040]\)	\(102949393183198/86815346805\)	\(-8364655564312084899840\)	\([2]\)	\(28311552\)	\(2.8942\)

^*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 476520cj1.

Rank

The elliptic curves in class 476520cj have rank \(0\).

Complex multiplication

The elliptic curves in class 476520cj do not have complex multiplication.

Modular form 476520.2.a.cj

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.