Elliptic curve isogeny class with LMFDB label 476850.hb (Cremona label 476850hb)

• Label: 476850.hb
• Number of curves: $4$
• Conductor: $476850$
• CM: no
• Rank: $1$

Elliptic curves in class 476850.hb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
476850.hb1	476850hb3	\([1, 1, 1, -4103420838, 101171886996531]\)	\(20260414982443110947641/720358602480\)	\(271682898001633923750000\)	\([2]\)	\(254803968\)	\(3.9924\)	\(\Gamma_0(N)\)-optimal^*
476850.hb2	476850hb2	\([1, 1, 1, -256830838, 1575978716531]\)	\(4967657717692586041/29490113030400\)	\(11122181845141860900000000\)	\([2, 2]\)	\(127401984\)	\(3.6458\)	\(\Gamma_0(N)\)-optimal^*
476850.hb3	476850hb4	\([1, 1, 1, -109440838, 3372368036531]\)	\(-384369029857072441/12804787777021680\)	\(-4829319507784647117123750000\)	\([2]\)	\(254803968\)	\(3.9924\)
476850.hb4	476850hb1	\([1, 1, 1, -25630838, -8203683469]\)	\(4937402992298041/2780405760000\)	\(1048628685624960000000000\)	\([2]\)	\(63700992\)	\(3.2992\)	\(\Gamma_0(N)\)-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 476850.hb1.

Rank

The elliptic curves in class 476850.hb have rank \(1\).

Complex multiplication

The elliptic curves in class 476850.hb do not have complex multiplication.

Modular form 476850.2.a.hb

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.