Elliptic curve isogeny class with Cremona label 6370ba (LMFDB label 6370.q)

• Label: 6370ba
• Number of curves: $1$
• Conductor: $6370$
• CM: no
• Rank: $1$

Rank

The elliptic curve 6370ba1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(5\)	\(1 - T\)
\(7\)	\(1\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 3 T + 29 T^{2}\)	1.29.ad
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 6370ba do not have complex multiplication.

Modular form 6370.2.a.ba

Elliptic curves in class 6370ba

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
6370.q1	6370ba1	\([1, 1, 1, -4075, 109017]\)	\(-21818208730807/2812160000\)	\(-964570880000\)	\([]\)	\(8448\)	\(1.0331\)	\(\Gamma_0(N)\)-optimal