Cremona's table of elliptic curves

83 = Prime conductor

Field	Data	Notes
Atkin-Lehner	83+	Signs for the Atkin-Lehner involutions
Class	83a	Isogeny class
Conductor	83	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	2	Modular degree for the optimal curve
Δ	-83 = Prime discriminant	Discriminant
Eigenvalues	-1 -1 -2 -3  3 -6  5  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,1,0]	[a1,a2,a3,a4,a6]
Generators	[0:0:1]	Generators of the group modulo torsion
j	103823/83	j-invariant
L	0.5982673327166	L(r)(E,1)/r!
Ω	3.374468900094	Real period
R	0.17729229411477	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1328e1 5312e1 747d1 2075a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 83a1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-1	-1	-2	-3	3	-6	5	2	-4	-7	5	-11	-2	-8	0	6	5	5	-2	2	0	14	+	0	-8

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Quadratic twists for elliptic curve 83a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	-83
1328e1	5312e1	747d1	2075a1	4067c1	10043c1	14027a1	23987b1	29963c1	43907b1	69803a1	79763d1	113627a1	6889a1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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