Elliptic curve isogeny class with LMFDB label 2142.r (Cremona label 2142m)

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

Rank

The elliptic curve 2142.r1 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 \(\mathbb{F}_p\)
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(13\)	\( 1 + 5 T + 13 T^{2}\)	1.13.f
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 + 4 T + 29 T^{2}\)	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 2142.2.a.r

Elliptic curves in class 2142.r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2142.r1	2142m1	\([1, -1, 1, 1402, 2485]\)	\(15494117157/9143008\)	\(-179961826464\)	\([]\)	\(2400\)	\(0.84903\)	\(\Gamma_0(N)\)-optimal