Elliptic curve isogeny class with Cremona label 2142c (LMFDB label 2142.f)

• Label: 2142c
• Number of curves: $1$
• Conductor: $2142$
• CM: no
• Rank: $1$

Rank

The elliptic curve 2142c1 has rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 2142c do not have complex multiplication.

Modular form 2142.2.a.c

Elliptic curves in class 2142c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2142.f1	2142c1	\([1, -1, 0, 156, -144]\)	\(15494117157/9143008\)	\(-246861216\)	\([]\)	\(800\)	\(0.29973\)	\(\Gamma_0(N)\)-optimal