Elliptic curve isogeny class with Cremona label 156702cm (LMFDB label 156702.c)

• Label: 156702cm
• Number of curves: $4$
• Conductor: $156702$
• CM: no
• Rank: $1$

Elliptic curves in class 156702cm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
156702.c4	156702cm1	\([1, 1, 0, -28151, -341739]\)	\(20972058349033/11736711168\)	\(1380812332204032\)	\([2]\)	\(829440\)	\(1.5953\)	\(\Gamma_0(N)\)-optimal
156702.c2	156702cm2	\([1, 1, 0, -279031, 56306965]\)	\(20421858870283753/128290046976\)	\(15093195736679424\)	\([2, 2]\)	\(1658880\)	\(1.9419\)
156702.c1	156702cm3	\([1, 1, 0, -4457751, 3620755125]\)	\(83268941223547539433/3317067936\)	\(390249725602464\)	\([2]\)	\(3317760\)	\(2.2885\)
156702.c3	156702cm4	\([1, 1, 0, -114391, 122393461]\)	\(-1407074115849193/54234808266912\)	\(-6380670957793929888\)	\([2]\)	\(3317760\)	\(2.2885\)

Rank

The elliptic curves in class 156702cm have rank \(1\).

Complex multiplication

The elliptic curves in class 156702cm do not have complex multiplication.

Modular form 156702.2.a.cm

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.