Elliptic curve isogeny class with Cremona label 12279a (LMFDB label 12279.a)

• Label: 12279a
• Number of curves: $1$
• Conductor: $12279$
• CM: no
• Rank: $3$

Rank

The elliptic curve 12279a1 has rank \(3\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1 + T\)
\(4093\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T + 2 T^{2}\)	1.2.c
\(5\)	\( 1 + 4 T + 5 T^{2}\)	1.5.e
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(11\)	\( 1 + 5 T + 11 T^{2}\)	1.11.f
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 + 7 T + 17 T^{2}\)	1.17.h
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + T + 29 T^{2}\)	1.29.b
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 12279a do not have complex multiplication.

Modular form 12279.2.a.a

Elliptic curves in class 12279a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
12279.a1	12279a1	\([0, -1, 1, -10, 12]\)	\(122023936/36837\)	\(36837\)	\([]\)	\(4320\)	\(-0.41865\)	\(\Gamma_0(N)\)-optimal