Elliptic curve isogeny class with LMFDB label 317130.bz (Cremona label 317130bz)

• Label: 317130.bz
• Number of curves: $1$
• Conductor: $317130$
• CM: no
• Rank: $1$

Rank

The elliptic curve 317130.bz1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 + T\)
\(5\)	\(1 - T\)
\(11\)	\(1 - T\)
\(31\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + T + 23 T^{2}\)	1.23.b
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 317130.bz do not have complex multiplication.

Modular form 317130.2.a.bz

Elliptic curves in class 317130.bz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
317130.bz1	317130bz1	\([1, 1, 1, -12228745, -16465141705]\)	\(-227876330943752401/6138000000\)	\(-5447497593978000000\)	\([]\)	\(15482880\)	\(2.6996\)	\(\Gamma_0(N)\)-optimal