Elliptic curve isogeny class with LMFDB label 142296.r (Cremona label 142296bc)

• Label: 142296.r
• Number of curves: $1$
• Conductor: $142296$
• CM: no
• Rank: $0$

Rank

The elliptic curve 142296.r1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(7\)	\(1\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(13\)	\( 1 - 3 T + 13 T^{2}\)	1.13.ad
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 7 T + 19 T^{2}\)	1.19.ah
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 - 9 T + 29 T^{2}\)	1.29.aj
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 142296.r do not have complex multiplication.

Modular form 142296.2.a.r

Elliptic curves in class 142296.r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
142296.r1	142296bc1	\([0, -1, 0, -9844116, 12316162377]\)	\(-31636584484096/1331669031\)	\(-4440794062909317180144\)	\([]\)	\(8294400\)	\(2.9203\)	\(\Gamma_0(N)\)-optimal