Elliptic curve isogeny class with LMFDB label 3870.z (Cremona label 3870y)

• Label: 3870.z
• Number of curves: $4$
• Conductor: $3870$
• CM: no
• Rank: $0$

Elliptic curves in class 3870.z

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
3870.z1	3870y3	[1, -1, 1, -7547, -248731]	[2]	6144
3870.z2	3870y2	[1, -1, 1, -797, 2369]	[2, 2]	3072
3870.z3	3870y1	[1, -1, 1, -617, 6041]	[4]	1536	\(\Gamma_0(N)\)-optimal
3870.z4	3870y4	[1, -1, 1, 3073, 16301]	[2]	6144

Rank

The elliptic curves in class 3870.z have rank \(0\).

Complex multiplication

The elliptic curves in class 3870.z do not have complex multiplication.

Modular form 3870.2.a.z

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.