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	3984d	Isogeny class
Conductor	3984	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	672	Modular degree for the optimal curve
Δ	4079616 = 214 · 3 · 83	Discriminant
Eigenvalues	2- 3+  2 -4  0  0 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-72,240]	[a1,a2,a3,a4,a6]
Generators	[2:10:1]	Generators of the group modulo torsion
j	10218313/996	j-invariant
L	3.1140165706901	L(r)(E,1)/r!
Ω	2.4011551866365	Real period
R	1.2968826788127	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	498a1 15936u1 11952p1 99600cy1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3984d1

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	0	-2	0	6	0	4	10	-2	-4	0	-14	-12	-6	0	-4	10	-2	-	-6	-10

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Quadratic twists for elliptic curve 3984d1

-4	8	-3	5
498a1	15936u1	11952p1	99600cy1

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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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