Elliptic curve isogeny class with LMFDB label 58121.c (Cremona label 58121b)

• Label: 58121.c
• Number of curves: $4$
• Conductor: $58121$
• CM: no
• Rank: $1$

Elliptic curves in class 58121.c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
58121.c1	58121b4	\([1, -1, 0, -44651, -3619606]\)	\(209267191953/55223\)	\(2598014686463\)	\([2]\)	\(138240\)	\(1.3666\)
58121.c2	58121b2	\([1, -1, 0, -3136, -41013]\)	\(72511713/25921\)	\(1219476281401\)	\([2, 2]\)	\(69120\)	\(1.0200\)
58121.c3	58121b1	\([1, -1, 0, -1331, 18552]\)	\(5545233/161\)	\(7574386841\)	\([2]\)	\(34560\)	\(0.67344\)	\(\Gamma_0(N)\)-optimal
58121.c4	58121b3	\([1, -1, 0, 9499, -296240]\)	\(2014698447/1958887\)	\(-92157564694447\)	\([2]\)	\(138240\)	\(1.3666\)

Rank

The elliptic curves in class 58121.c have rank \(1\).

Complex multiplication

The elliptic curves in class 58121.c do not have complex multiplication.

Modular form 58121.2.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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.