Elliptic curve isogeny class with LMFDB label 10010.e (Cremona label 10010j)

• Label: 10010.e
• Number of curves: $2$
• Conductor: $10010$
• CM: no
• Rank: $1$

Elliptic curves in class 10010.e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
10010.e1	10010j2	\([1, -1, 0, -224, 168]\)	\(1246114341081/715715000\)	\(715715000\)	\([2]\)	\(4608\)	\(0.38870\)
10010.e2	10010j1	\([1, -1, 0, 56, 0]\)	\(19227292839/11211200\)	\(-11211200\)	\([2]\)	\(2304\)	\(0.042130\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 10010.e have rank \(1\).

Complex multiplication

The elliptic curves in class 10010.e do not have complex multiplication.

Modular form 10010.2.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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.