Cremona's table of elliptic curves

996 = 2² · 3 · 83

Field	Data	Notes
Atkin-Lehner	2- 3- 83+	Signs for the Atkin-Lehner involutions
Class	996c	Isogeny class
Conductor	996	Conductor
∏ cp	1	Product of Tamagawa factors cp
Δ	-439132416 = -1 · 28 · 3 · 833	Discriminant
Eigenvalues	2- 3- -3  2 -3 -4  0 -7	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,108,-876]	[a1,a2,a3,a4,a6]
Generators	[11:42:1]	Generators of the group modulo torsion
j	539172272/1715361	j-invariant
L	2.5309557846901	L(r)(E,1)/r!
Ω	0.85486721361681	Real period
R	2.9606420089291	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	3984e2 15936g2 2988b2 24900d2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 996c2

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
-	-	-3	2	-3	-4	0	-7	-3	-6	8	11	0	-4	-12	-3	-9	-1	-13	6	-10	8	+	3	8

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Quadratic twists for elliptic curve 996c2

-4	8	-3	5	-7	-11	-83
3984e2	15936g2	2988b2	24900d2	48804n2	120516n2	82668c2

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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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