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	3984c	Isogeny class
Conductor	3984	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	2496	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	[-15:52:1]	Generators of the group modulo torsion
j	1893932336/132328809	j-invariant
L	3.1174770424522	L(r)(E,1)/r!
Ω	0.88861456344947	Real period
R	3.508244373523	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	996b1 15936t1 11952k1 99600cw1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3984c1

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 3984c1

-4	8	-3	5
996b1	15936t1	11952k1	99600cw1

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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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