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

• Label: 2420.e
• Number of curves: $2$
• Conductor: $2420$
• CM: no
• Rank: $1$

Rank

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

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1 + T\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - T + 3 T^{2}\)	1.3.ab
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 2420.2.a.e

Isogeny matrix

The \((i,j)\)-th 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 2420.e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2420.e1	2420d2	\([0, 1, 0, -52796, -4688620]\)	\(-296587984/125\)	\(-6859484192000\)	\([]\)	\(4752\)	\(1.4242\)
2420.e2	2420d1	\([0, 1, 0, 444, -24796]\)	\(176/5\)	\(-274379367680\)	\([3]\)	\(1584\)	\(0.87489\)	\(\Gamma_0(N)\)-optimal