Elliptic curve isogeny class with LMFDB label 187395.bd (Cremona label 187395z)

• Label: 187395.bd
• Number of curves: $1$
• Conductor: $187395$
• CM: no
• Rank: $1$

Rank

The elliptic curve 187395.bd1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1 - T\)
\(5\)	\(1 - T\)
\(13\)	\(1 - T\)
\(31\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 - 2 T + 2 T^{2}\)	1.2.ac
\(7\)	\( 1 - 3 T + 7 T^{2}\)	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.c
\(23\)	\( 1 - 3 T + 23 T^{2}\)	1.23.ad
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 187395.bd do not have complex multiplication.

Modular form 187395.2.a.bd

Elliptic curves in class 187395.bd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
187395.bd1	187395z1	\([0, 1, 1, -182910, -30979339]\)	\(-762549907456/24024195\)	\(-21321561495561795\)	\([]\)	\(2489760\)	\(1.9096\)	\(\Gamma_0(N)\)-optimal