Elliptic curve isogeny class with Cremona label 471510g (LMFDB label 471510.g)

• Label: 471510g
• Number of curves: $4$
• Conductor: $471510$
• CM: no
• Rank: $1$

Elliptic curves in class 471510g

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
471510.g3	471510g1	\([1, -1, 0, -550380, -64306800]\)	\(141477771269043/68107000000\)	\(8875965975201000000\)	\([2]\)	\(9289728\)	\(2.3295\)	\(\Gamma_0(N)\)-optimal
471510.g4	471510g2	\([1, -1, 0, 1984620, -491707800]\)	\(6633333032010957/4638563449000\)	\(-604515414673014507000\)	\([2]\)	\(18579456\)	\(2.6761\)
471510.g1	471510g3	\([1, -1, 0, -36800880, -85918892500]\)	\(58015885327629867/38728300\)	\(3679424027976680100\)	\([2]\)	\(27869184\)	\(2.8788\)
471510.g2	471510g4	\([1, -1, 0, -36572730, -87036964390]\)	\(-56943538625741067/1499881220890\)	\(-142497837582689259916830\)	\([2]\)	\(55738368\)	\(3.2254\)

Rank

The elliptic curves in class 471510g have rank \(1\).

Complex multiplication

The elliptic curves in class 471510g do not have complex multiplication.

Modular form 471510.2.a.g

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.