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	1007681536 = 220 · 312	Discriminant
Eigenvalues	2+  0  2  0  0 -2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1324,18480]	[a1,a2,a3,a4,a6]
Generators	[120:1260:1]	Generators of the group modulo torsion
j	979146657/3844	j-invariant
L	3.1937522979254	L(r)(E,1)/r!
Ω	1.5679960790381	Real period
R	4.0736738319966	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	1984j2 62a2 17856q2 49600a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1984b2

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 1984b2

-4	8	-3	5	-7	-31
1984j2	62a2	17856q2	49600a2	97216s2	61504k2

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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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