Elliptic curve isogeny class with Cremona label 116032r (LMFDB label 116032.h)

• Label: 116032r
• Number of curves: $1$
• Conductor: $116032$
• CM: no
• Rank: $1$

Rank

The elliptic curve 116032r1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(7\)	\(1\)
\(37\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 116032r do not have complex multiplication.

Modular form 116032.2.a.r

Elliptic curves in class 116032r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
116032.h1	116032r1	\([0, 1, 0, -751, -8457]\)	\(-6229504/259\)	\(-1950149824\)	\([]\)	\(49152\)	\(0.54959\)	\(\Gamma_0(N)\)-optimal