Cremona's table of elliptic curves

1984 = 2⁶ · 31

Field	Data	Notes
Atkin-Lehner	2+ 31+	Signs for the Atkin-Lehner involutions
Class	1984b	Isogeny class
Conductor	1984	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	484190978048 = 219 · 314	Discriminant
Eigenvalues	2+  0  2  0  0 -2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1964,-1232]	[a1,a2,a3,a4,a6]
Generators	[54:224:1]	Generators of the group modulo torsion
j	3196010817/1847042	j-invariant
L	3.1937522979254	L(r)(E,1)/r!
Ω	0.78399803951905	Real period
R	2.0368369159983	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	1984j4 62a3 17856q4 49600a3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1984b3

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

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Quadratic twists for elliptic curve 1984b3

-4	8	-3	5	-7	-31
1984j4	62a3	17856q4	49600a3	97216s3	61504k3

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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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