Elliptic curve isogeny class with LMFDB label 4002.a (Cremona label 4002c)

• Label: 4002.a
• Number of curves: $2$
• Conductor: $4002$
• CM: no
• Rank: $2$

Elliptic curves in class 4002.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
4002.a1	4002c2	\([1, 1, 0, -3711, 85485]\)	\(5654307459987577/368184\)	\(368184\)	\([2]\)	\(2688\)	\(0.52612\)
4002.a2	4002c1	\([1, 1, 0, -231, 1269]\)	\(-1372441819897/11141568\)	\(-11141568\)	\([2]\)	\(1344\)	\(0.17955\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 4002.a have rank \(2\).

Complex multiplication

The elliptic curves in class 4002.a do not have complex multiplication.

Modular form 4002.2.a.a

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.