Cremona's table of elliptic curves

5082 = 2 · 3 · 7 · 11²

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 11+	Signs for the Atkin-Lehner involutions
Class	5082y	Isogeny class
Conductor	5082	Conductor
∏ cp	60	Product of Tamagawa factors cp
deg	2880	Modular degree for the optimal curve
Δ	-257596416 = -1 · 210 · 33 · 7 · 113	Discriminant
Eigenvalues	2- 3- -2 7+ 11+ -6  0  8	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-74,804]	[a1,a2,a3,a4,a6]
Generators	[4:22:1]	Generators of the group modulo torsion
j	-33698267/193536	j-invariant
L	5.7161903755199	L(r)(E,1)/r!
Ω	1.511001814671	Real period
R	0.25220311098764	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	40656bp1 15246f1 127050q1 35574bs1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5082y1

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
-	-	-2	+	+	-6	0	8	-6	2	10	-6	-4	2	-8	0	-12	-2	-12	-14	-10	0	-14	10	2

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Quadratic twists for elliptic curve 5082y1

-4	-3	5	-7	-11
40656bp1	15246f1	127050q1	35574bs1	5082l1

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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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