Elliptic curve isogeny class with Cremona label 446160jg (LMFDB label 446160.jg)

• Label: 446160jg
• Number of curves: $4$
• Conductor: $446160$
• CM: no
• Rank: $0$

Elliptic curves in class 446160jg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
446160.jg4	446160jg1	\([0, 1, 0, 58080, 306688500]\)	\(1095912791/2055596400\)	\(-40640394051123609600\)	\([2]\)	\(12386304\)	\(2.4416\)	\(\Gamma_0(N)\)-optimal^*
446160.jg3	446160jg2	\([0, 1, 0, -6485600, 6219557748]\)	\(1525998818291689/37268302500\)	\(736817061567375360000\)	\([2, 2]\)	\(24772608\)	\(2.7881\)	\(\Gamma_0(N)\)-optimal^*
446160.jg1	446160jg3	\([0, 1, 0, -103153600, 403215700148]\)	\(6139836723518159689/3799803150\)	\(75124424878687641600\)	\([4]\)	\(49545216\)	\(3.1347\)	\(\Gamma_0(N)\)-optimal^*
446160.jg2	446160jg4	\([0, 1, 0, -14516480, -12248253900]\)	\(17111482619973769/6627044531250\)	\(131020710653289600000000\)	\([2]\)	\(49545216\)	\(3.1347\)

^*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 446160jg1.

Rank

The elliptic curves in class 446160jg have rank \(0\).

Complex multiplication

The elliptic curves in class 446160jg do not have complex multiplication.

Modular form 446160.2.a.jg

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.