Cremona's table of elliptic curves

1984 = 2⁶ · 31

Field	Data	Notes
Atkin-Lehner	2+ 31+	Signs for the Atkin-Lehner involutions
Class	1984a	Isogeny class
Conductor	1984	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	-31744 = -1 · 210 · 31	Discriminant
Eigenvalues	2+  0 -1  3 -6  4  0  5	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-68,-216]	[a1,a2,a3,a4,a6]
Generators	[29:149:1]	Generators of the group modulo torsion
j	-33958656/31	j-invariant
L	2.9253515030062	L(r)(E,1)/r!
Ω	0.83122492450629	Real period
R	3.5193260172555	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	1984i1 124b1 17856k1 49600e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1984a1

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	-1	3	-6	4	0	5	-4	-2	+	2	-9	-2	4	-12	-9	-12	12	5	-14	10	-2	6	-7

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Quadratic twists for elliptic curve 1984a1

-4	8	-3	5	-7	-31
1984i1	124b1	17856k1	49600e1	97216p1	61504j1

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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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