Elliptic curve isogeny class with LMFDB label 4896.e (Cremona label 4896b)

• Label: 4896.e
• Number of curves: $4$
• Conductor: $4896$
• CM: no
• Rank: $0$

Elliptic curves in class 4896.e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
4896.e1	4896b3	\([0, 0, 0, -14691, 685370]\)	\(939464338184/153\)	\(57106944\)	\([2]\)	\(4096\)	\(0.89001\)
4896.e2	4896b2	\([0, 0, 0, -1731, -10906]\)	\(1536800264/751689\)	\(280566415872\)	\([2]\)	\(4096\)	\(0.89001\)
4896.e3	4896b1	\([0, 0, 0, -921, 10640]\)	\(1851804352/23409\)	\(1092170304\)	\([2, 2]\)	\(2048\)	\(0.54343\)	\(\Gamma_0(N)\)-optimal
4896.e4	4896b4	\([0, 0, 0, -156, 27776]\)	\(-140608/111537\)	\(-333047697408\)	\([2]\)	\(4096\)	\(0.89001\)

Rank

The elliptic curves in class 4896.e have rank \(0\).

Complex multiplication

The elliptic curves in class 4896.e do not have complex multiplication.

Modular form 4896.2.a.e

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.