Elliptic curve isogeny class with LMFDB label 400.c (Cremona label 400e)

• Label: 400.c
• Number of curves: $4$
• Conductor: $400$
• CM: no
• Rank: $0$

Elliptic curves in class 400.c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
400.c1	400e3	\([0, 1, 0, -1033, 12438]\)	\(488095744/125\)	\(31250000\)	\([2]\)	\(144\)	\(0.42408\)
400.c2	400e4	\([0, 1, 0, -908, 15688]\)	\(-20720464/15625\)	\(-62500000000\)	\([2]\)	\(288\)	\(0.77065\)
400.c3	400e1	\([0, 1, 0, -33, -62]\)	\(16384/5\)	\(1250000\)	\([2]\)	\(48\)	\(-0.12523\)	\(\Gamma_0(N)\)-optimal
400.c4	400e2	\([0, 1, 0, 92, -312]\)	\(21296/25\)	\(-100000000\)	\([2]\)	\(96\)	\(0.22134\)

Rank

The elliptic curves in class 400.c have rank \(0\).

Complex multiplication

The elliptic curves in class 400.c do not have complex multiplication.

Modular form 400.2.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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.