Elliptic curve isogeny class with LMFDB label 215985.l (Cremona label 215985ba)

• Label: 215985.l
• Number of curves: $4$
• Conductor: $215985$
• CM: no
• Rank: $1$

Elliptic curves in class 215985.l

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
215985.l1	215985ba3	\([1, 1, 1, -385811, 92070254]\)	\(3585019225176649/316207395\)	\(560180688893595\)	\([2]\)	\(1966080\)	\(1.8708\)
215985.l2	215985ba4	\([1, 1, 1, -140181, -19232322]\)	\(171963096231529/9865918125\)	\(17478075779443125\)	\([2]\)	\(1966080\)	\(1.8708\)
215985.l3	215985ba2	\([1, 1, 1, -25836, 1212564]\)	\(1076575468249/258084225\)	\(457211947725225\)	\([2, 2]\)	\(983040\)	\(1.5242\)
215985.l4	215985ba1	\([1, 1, 1, 3809, 121628]\)	\(3449795831/5510295\)	\(-9761823720495\)	\([2]\)	\(491520\)	\(1.1776\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 215985.l have rank \(1\).

Complex multiplication

The elliptic curves in class 215985.l do not have complex multiplication.

Modular form 215985.2.a.l

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.