Elliptic curve isogeny class with LMFDB label 163995.g (Cremona label 163995c)

• Label: 163995.g
• Number of curves: $1$
• Conductor: $163995$
• CM: no
• Rank: $1$

Rank

The elliptic curve 163995.g1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1 - T\)
\(5\)	\(1 - T\)
\(13\)	\(1 + T\)
\(29\)	\(1\)

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
\(11\)	\( 1 - T + 11 T^{2}\)	1.11.ab
\(17\)	\( 1 - T + 17 T^{2}\)	1.17.ab
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 3 T + 23 T^{2}\)	1.23.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 163995.g do not have complex multiplication.

Modular form 163995.2.a.g

Elliptic curves in class 163995.g

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
163995.g1	163995c1	\([0, 1, 1, -160070, 25258586]\)	\(-762549907456/24024195\)	\(-14290151454251595\)	\([]\)	\(2107392\)	\(1.8762\)	\(\Gamma_0(N)\)-optimal