Elliptic curve isogeny class with Cremona label 331545n (LMFDB label 331545.n)

• Label: 331545n
• Number of curves: $4$
• Conductor: $331545$
• CM: no
• Rank: $1$

Elliptic curves in class 331545n

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
331545.n4	331545n1	\([1, 1, 0, 438677, -70219592]\)	\(10519294081031/8500170375\)	\(-7543932496939650375\)	\([2]\)	\(8640000\)	\(2.3101\)	\(\Gamma_0(N)\)-optimal
331545.n3	331545n2	\([1, 1, 0, -2103168, -613666053]\)	\(1159246431432649/488076890625\)	\(433170037040721890625\)	\([2, 2]\)	\(17280000\)	\(2.6567\)
331545.n2	331545n3	\([1, 1, 0, -15917543, 24011838822]\)	\(502552788401502649/10024505152875\)	\(8896785223380030232875\)	\([2]\)	\(34560000\)	\(3.0033\)
331545.n1	331545n4	\([1, 1, 0, -28958313, -59968907532]\)	\(3026030815665395929/1364501953125\)	\(1211000506130126953125\)	\([2]\)	\(34560000\)	\(3.0033\)

Rank

The elliptic curves in class 331545n have rank \(1\).

Complex multiplication

The elliptic curves in class 331545n do not have complex multiplication.

Modular form 331545.2.a.n

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.