Elliptic curve isogeny class with LMFDB label 420.c (Cremona label 420c)

• Label: 420.c
• Number of curves: $4$
• Conductor: $420$
• CM: no
• Rank: $0$

Elliptic curves in class 420.c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
420.c1	420c3	\([0, 1, 0, -301, -1960]\)	\(189123395584/16078125\)	\(257250000\)	\([2]\)	\(216\)	\(0.35520\)
420.c2	420c1	\([0, 1, 0, -61, 164]\)	\(1594753024/4725\)	\(75600\)	\([6]\)	\(72\)	\(-0.19410\)	\(\Gamma_0(N)\)-optimal
420.c3	420c2	\([0, 1, 0, -36, 324]\)	\(-20720464/178605\)	\(-45722880\)	\([6]\)	\(144\)	\(0.15247\)
420.c4	420c4	\([0, 1, 0, 324, -8460]\)	\(14647977776/132355125\)	\(-33882912000\)	\([2]\)	\(432\)	\(0.70178\)

Rank

The elliptic curves in class 420.c have rank \(0\).

Complex multiplication

The elliptic curves in class 420.c do not have complex multiplication.

Modular form 420.2.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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels.