Elliptic curve isogeny class with Cremona label 345c (LMFDB label 345.e)

• Label: 345c
• Number of curves: $4$
• Conductor: $345$
• CM: no
• Rank: $0$

Elliptic curves in class 345c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
345.e4	345c1	\([1, 0, 1, 456, 2401]\)	\(10519294081031/8500170375\)	\(-8500170375\)	\([2]\)	\(300\)	\(0.59313\)	\(\Gamma_0(N)\)-optimal
345.e3	345c2	\([1, 0, 1, -2189, 20387]\)	\(1159246431432649/488076890625\)	\(488076890625\)	\([2, 2]\)	\(600\)	\(0.93970\)
345.e2	345c3	\([1, 0, 1, -16564, -807613]\)	\(502552788401502649/10024505152875\)	\(10024505152875\)	\([2]\)	\(1200\)	\(1.2863\)
345.e1	345c4	\([1, 0, 1, -30134, 2010071]\)	\(3026030815665395929/1364501953125\)	\(1364501953125\)	\([2]\)	\(1200\)	\(1.2863\)

Rank

The elliptic curves in class 345c have rank \(0\).

Complex multiplication

The elliptic curves in class 345c do not have complex multiplication.

Modular form 345.2.a.c

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.