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	996a	Isogeny class
Conductor	996	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	47616768 = 28 · 33 · 832	Discriminant
Eigenvalues	2- 3+  4  4  4 -2  6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-116,-312]	[a1,a2,a3,a4,a6]
j	680136784/186003	j-invariant
L	2.2253481844848	L(r)(E,1)/r!
Ω	1.4835654563232	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3984h2 15936n2 2988c2 24900o2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 996a2

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

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Quadratic twists for elliptic curve 996a2

-4	8	-3	5	-7	-11	-83
3984h2	15936n2	2988c2	24900o2	48804w2	120516d2	82668a2

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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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