Elliptic curve isogeny class with Cremona label 131904bb (LMFDB label 131904.c)

• Label: 131904bb
• Number of curves: $1$
• Conductor: $131904$
• CM: no
• Rank: $2$

Rank

The elliptic curve 131904bb1 has rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(229\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 + 9 T + 29 T^{2}\)	1.29.j
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 131904bb do not have complex multiplication.

Modular form 131904.2.a.bb

Elliptic curves in class 131904bb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
131904.c1	131904bb1	\([0, 0, 0, -984, -11864]\)	\(141150208/229\)	\(170947584\)	\([]\)	\(84480\)	\(0.47665\)	\(\Gamma_0(N)\)-optimal