Elliptic curve isogeny class with LMFDB label 660.c (Cremona label 660c)

• Label: 660.c
• Number of curves: $4$
• Conductor: $660$
• CM: no
• Rank: $1$

Elliptic curves in class 660.c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
660.c1	660c4	\([0, 1, 0, -1556, -13356]\)	\(1628514404944/664335375\)	\(170069856000\)	\([2]\)	\(864\)	\(0.85261\)
660.c2	660c2	\([0, 1, 0, -716, 7140]\)	\(158792223184/16335\)	\(4181760\)	\([6]\)	\(288\)	\(0.30330\)
660.c3	660c1	\([0, 1, 0, -41, 120]\)	\(-488095744/200475\)	\(-3207600\)	\([6]\)	\(144\)	\(-0.043272\)	\(\Gamma_0(N)\)-optimal
660.c4	660c3	\([0, 1, 0, 319, -1356]\)	\(223673040896/187171875\)	\(-2994750000\)	\([2]\)	\(432\)	\(0.50603\)

Rank

The elliptic curves in class 660.c have rank \(1\).

Complex multiplication

The elliptic curves in class 660.c do not have complex multiplication.

Modular form 660.2.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.