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	5082a	Isogeny class
Conductor	5082	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	42240	Modular degree for the optimal curve
Δ	17391920351511552 = 210 · 3 · 74 · 119	Discriminant
Eigenvalues	2+ 3+  0 7+ 11+  2 -2  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-213930,37463892]	[a1,a2,a3,a4,a6]
Generators	[-508:4174:1]	Generators of the group modulo torsion
j	459206250875/7375872	j-invariant
L	2.3276626678691	L(r)(E,1)/r!
Ω	0.38996929069265	Real period
R	2.9844179060033	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	40656cv1 15246be1 127050ho1 35574u1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5082a1

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	-2	2	-2	10	-4	-2	2	-6	-10	12	4	2	-12	2	4	-4	8	-6	6

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Quadratic twists for elliptic curve 5082a1

-4	-3	5	-7	-11
40656cv1	15246be1	127050ho1	35574u1	5082s1

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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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