Elliptic curve isogeny class with Cremona label 357390g (LMFDB label 357390.g)

• Label: 357390g
• Number of curves: $4$
• Conductor: $357390$
• CM: no
• Rank: $1$

Elliptic curves in class 357390g

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
357390.g3	357390g1	\([1, -1, 0, -565935, 34852525]\)	\(15781142246787/8722841600\)	\(11080091733177139200\)	\([2]\)	\(12317184\)	\(2.3448\)	\(\Gamma_0(N)\)-optimal
357390.g4	357390g2	\([1, -1, 0, 2206545, 273840301]\)	\(935355271080573/566899520000\)	\(-720097758635682240000\)	\([2]\)	\(24634368\)	\(2.6914\)
357390.g1	357390g3	\([1, -1, 0, -34875375, 79281780461]\)	\(5066026756449723/11000000\)	\(10186044832953000000\)	\([2]\)	\(36951552\)	\(2.8941\)
357390.g2	357390g4	\([1, -1, 0, -34485495, 81140650325]\)	\(-4898016158612283/236328125000\)	\(-218840806957974609375000\)	\([2]\)	\(73903104\)	\(3.2407\)

Rank

The elliptic curves in class 357390g have rank \(1\).

Complex multiplication

The elliptic curves in class 357390g do not have complex multiplication.

Modular form 357390.2.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.