Elliptic curve isogeny class with LMFDB label 12138.k (Cremona label 12138g)

• Label: 12138.k
• Number of curves: $1$
• Conductor: $12138$
• CM: no
• Rank: $0$

Rank

The elliptic curve 12138.k1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1 - T\)
\(7\)	\(1 + T\)
\(17\)	\(1\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 12138.k do not have complex multiplication.

Modular form 12138.2.a.k

Elliptic curves in class 12138.k

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
12138.k1	12138g1	\([1, 0, 1, -4218684, -3343946630]\)	\(-344002044213921241/1011143540736\)	\(-24406546983419510784\)	\([]\)	\(587520\)	\(2.5904\)	\(\Gamma_0(N)\)-optimal