Cremona's table of elliptic curves

1494 = 2 · 3² · 83

Field	Data	Notes
Atkin-Lehner	2- 3+ 83-	Signs for the Atkin-Lehner involutions
Class	1494b	Isogeny class
Conductor	1494	Conductor
∏ cp	20	Product of Tamagawa factors cp
deg	160	Modular degree for the optimal curve
Δ	-2294784 = -1 · 210 · 33 · 83	Discriminant
Eigenvalues	2- 3+ -1 -2 -1 -2  0 -5	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-8,75]	[a1,a2,a3,a4,a6]
Generators	[5:-15:1]	Generators of the group modulo torsion
j	-1860867/84992	j-invariant
L	3.5959057179416	L(r)(E,1)/r!
Ω	2.1507285014963	Real period
R	0.083597388406762	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	11952g1 47808a1 1494a1 37350b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1494b1

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	-1	-2	0	-5	-7	6	-2	1	0	-4	6	-1	-3	-7	-7	-10	-4	0	-	11	12

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Quadratic twists for elliptic curve 1494b1

-4	8	-3	5	-7	-83
11952g1	47808a1	1494a1	37350b1	73206bb1	124002c1

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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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