Elliptic curve isogeny class with LMFDB label 2912.a (Cremona label 2912c)

• Label: 2912.a
• Number of curves: $1$
• Conductor: $2912$
• CM: no
• Rank: $1$

Rank

The elliptic curve 2912.a1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(7\)	\(1 - T\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(11\)	\( 1 - T + 11 T^{2}\)	1.11.ab
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 + 5 T + 23 T^{2}\)	1.23.f
\(29\)	\( 1 - 8 T + 29 T^{2}\)	1.29.ai
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 2912.a do not have complex multiplication.

Modular form 2912.2.a.a

Isogeny graph

Elliptic curves in class 2912.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2912.a1	2912c1	\([0, -1, 0, 632, 2324]\)	\(54439939000/36924979\)	\(-18905589248\)	\([]\)	\(1440\)	\(0.66056\)	\(\Gamma_0(N)\)-optimal