Cremona's table of elliptic curves

3984 = 2⁴ · 3 · 83

Field	Data	Notes
Atkin-Lehner	2+ 3+ 83+	Signs for the Atkin-Lehner involutions
Class	3984a	Isogeny class
Conductor	3984	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1248	Modular degree for the optimal curve
Δ	2294784 = 210 · 33 · 83	Discriminant
Eigenvalues	2+ 3+ -2  4  0 -4  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-744,8064]	[a1,a2,a3,a4,a6]
Generators	[14:14:1]	Generators of the group modulo torsion
j	44537533348/2241	j-invariant
L	3.0268748628138	L(r)(E,1)/r!
Ω	2.4446383975898	Real period
R	1.2381687474917	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1992a1 15936x1 11952f1 99600bd1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3984a1

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

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Quadratic twists for elliptic curve 3984a1

-4	8	-3	5
1992a1	15936x1	11952f1	99600bd1

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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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