Elliptic curve isogeny class with LMFDB label 2420.a (Cremona label 2420e)

• Label: 2420.a
• Number of curves: $4$
• Conductor: $2420$
• CM: no
• Rank: $1$

Elliptic curves in class 2420.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2420.a1	2420e3	\([0, 1, 0, -5001, 134440]\)	\(488095744/125\)	\(3543122000\)	\([2]\)	\(2160\)	\(0.81830\)
2420.a2	2420e4	\([0, 1, 0, -4396, 168804]\)	\(-20720464/15625\)	\(-7086244000000\)	\([2]\)	\(4320\)	\(1.1649\)
2420.a3	2420e1	\([0, 1, 0, -161, -596]\)	\(16384/5\)	\(141724880\)	\([2]\)	\(720\)	\(0.26900\)	\(\Gamma_0(N)\)-optimal
2420.a4	2420e2	\([0, 1, 0, 444, -3500]\)	\(21296/25\)	\(-11337990400\)	\([2]\)	\(1440\)	\(0.61557\)

Rank

The elliptic curves in class 2420.a have rank \(1\).

Complex multiplication

The elliptic curves in class 2420.a do not have complex multiplication.

Modular form 2420.2.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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.