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
deg	270	Modular degree for the optimal curve
Δ	-968112 = -1 · 24 · 36 · 83	Discriminant
Eigenvalues	2- 3+  4  4  4 -2  6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,19,-42]	[a1,a2,a3,a4,a6]
j	44957696/60507	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	3984h1 15936n1 2988c1 24900o1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 996a1

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 996a1

-4	8	-3	5	-7	-11	-83
3984h1	15936n1	2988c1	24900o1	48804w1	120516d1	82668a1

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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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