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	996b	Isogeny class
Conductor	996	Conductor
∏ cp	39	Product of Tamagawa factors cp
deg	624	Modular degree for the optimal curve
Δ	-33876175104 = -1 · 28 · 313 · 83	Discriminant
Eigenvalues	2- 3- -1 -2 -3  0 -8  3	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,164,-8764]	[a1,a2,a3,a4,a6]
Generators	[20:54:1]	Generators of the group modulo torsion
j	1893932336/132328809	j-invariant
L	2.5867487904047	L(r)(E,1)/r!
Ω	0.55494293667122	Real period
R	0.11952020231038	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	3984c1 15936d1 2988a1 24900c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 996b1

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	-2	-3	0	-8	3	-3	6	-4	-5	-8	4	0	7	-9	-9	9	-2	10	8	+	-15	8

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Quadratic twists for elliptic curve 996b1

-4	8	-3	5	-7	-11	-83
3984c1	15936d1	2988a1	24900c1	48804m1	120516i1	82668b1

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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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