Elliptic curve isogeny class with Cremona label 4002j (LMFDB label 4002.i)

• Label: 4002j
• Number of curves: $2$
• Conductor: $4002$
• CM: no
• Rank: $1$

Elliptic curves in class 4002j

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
4002.i2	4002j1	\([1, 1, 1, -109, -10333]\)	\(-143301984337/45635862528\)	\(-45635862528\)	\([2]\)	\(3456\)	\(0.72451\)	\(\Gamma_0(N)\)-optimal
4002.i1	4002j2	\([1, 1, 1, -7789, -265309]\)	\(52260349338689617/574696932864\)	\(574696932864\)	\([2]\)	\(6912\)	\(1.0711\)

Rank

The elliptic curves in class 4002j have rank \(1\).

Complex multiplication

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

Modular form 4002.2.a.j

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 Cremona numbering.

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

Isogeny graph

The vertices are labelled with Cremona labels.