Cremona's table of elliptic curves

83664 = 2⁴ · 3² · 7 · 83

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 83-	Signs for the Atkin-Lehner involutions
Class	83664cj	Isogeny class
Conductor	83664	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	-462908226644656128 = -1 · 214 · 310 · 78 · 83	Discriminant
Eigenvalues	2- 3- -2 7-  4 -2  6  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,190149,-7280534]	[a1,a2,a3,a4,a6]
Generators	[381:10976:1]	Generators of the group modulo torsion
j	254635161402887/155027028492	j-invariant
L	6.2793704767966	L(r)(E,1)/r!
Ω	0.17170305686036	Real period
R	1.1428470233662	Regulator
r	1	Rank of the group of rational points
S	0.99999999981732	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	10458s4 27888bj3	Quadratic twists by: -4 -3

Hecke Eigenvalues for elliptic curve 83664cj3

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
-	-	-2	-	4	-2	6	0	0	2	-8	6	-10	-8	-8	6	12	-2	8	0	10	12	-	-14	2

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Quadratic twists for elliptic curve 83664cj3

-4	-3
10458s4	27888bj3

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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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