Elliptic curve isogeny class with LMFDB label 83.a (Cremona label 83a)

• Label: 83.a
• Number of curves: $1$
• Conductor: $83$
• CM: no
• Rank: $1$

Rank

The elliptic curve 83.a1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(83\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + T + 2 T^{2}\)	1.2.b
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 - 5 T + 17 T^{2}\)	1.17.af
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 7 T + 29 T^{2}\)	1.29.h
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 83.a do not have complex multiplication.

Modular form 83.2.a.a

Isogeny graph

Elliptic curves in class 83.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
83.a1	83a1	\([1, 1, 1, 1, 0]\)	\(103823/83\)	\(-83\)	\([]\)	\(2\)	\(-0.94387\)	\(\Gamma_0(N)\)-optimal