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	4	Product of Tamagawa factors cp
Δ	16252928 = 219 · 31	Discriminant
Eigenvalues	2+  0  2  0  0 -2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-21164,1185072]	[a1,a2,a3,a4,a6]
Generators	[105336:779660:729]	Generators of the group modulo torsion
j	3999236143617/62	j-invariant
L	3.1937522979254	L(r)(E,1)/r!
Ω	1.5679960790381	Real period
R	8.1473476639931	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	1984j3 62a4 17856q3 49600a4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1984b4

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 1984b4

-4	8	-3	5	-7	-31
1984j3	62a4	17856q3	49600a4	97216s4	61504k4

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

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