Elliptic curve isogeny class with LMFDB label 975.b (Cremona label 975b)

• Label: 975.b
• Number of curves: $1$
• Conductor: $975$
• CM: no
• Rank: $1$

Rank

The elliptic curve 975.b1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1 + T\)
\(5\)	\(1\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T + 2 T^{2}\)	1.2.c
\(7\)	\( 1 - 3 T + 7 T^{2}\)	1.7.ad
\(11\)	\( 1 + 5 T + 11 T^{2}\)	1.11.f
\(17\)	\( 1 + 5 T + 17 T^{2}\)	1.17.f
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 - T + 23 T^{2}\)	1.23.ab
\(29\)	\( 1 - 10 T + 29 T^{2}\)	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 975.b do not have complex multiplication.

Modular form 975.2.a.b

Elliptic curves in class 975.b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
975.b1	975b1	\([0, -1, 1, -8, -82]\)	\(-4096/195\)	\(-3046875\)	\([]\)	\(288\)	\(-0.075866\)	\(\Gamma_0(N)\)-optimal