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	5082i	Isogeny class
Conductor	5082	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	446433372 = 22 · 32 · 7 · 116	Discriminant
Eigenvalues	2+ 3+ -2 7- 11- -6 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-162626,-25310424]	[a1,a2,a3,a4,a6]
Generators	[523:5486:1]	Generators of the group modulo torsion
j	268498407453697/252	j-invariant
L	2.0115011442453	L(r)(E,1)/r!
Ω	0.23773970088531	Real period
R	4.2304695781873	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	40656co4 15246bs4 127050hk4 35574bg4	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5082i3

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

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Quadratic twists for elliptic curve 5082i3

-4	-3	5	-7	-11
40656co4	15246bs4	127050hk4	35574bg4	42a4

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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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