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	5082k	Isogeny class
Conductor	5082	Conductor
∏ cp	120	Product of Tamagawa factors cp
deg	84480	Modular degree for the optimal curve
Δ	-158777907364935936 = -1 · 28 · 310 · 72 · 118	Discriminant
Eigenvalues	2+ 3- -3 7+ 11-  3 -5  6	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-139395,-27739010]	[a1,a2,a3,a4,a6]
Generators	[1583:-61776:1]	Generators of the group modulo torsion
j	-1397395501513/740710656	j-invariant
L	2.7285551501009	L(r)(E,1)/r!
Ω	0.12054399609517	Real period
R	0.18862788957339	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	40656bw1 15246bk1 127050gf1 35574p1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5082k1

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
+	-	-3	+	-	3	-5	6	-4	3	-2	1	11	-10	-6	-1	-6	10	8	-2	-6	14	-8	3	-15

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Quadratic twists for elliptic curve 5082k1

-4	-3	5	-7	-11
40656bw1	15246bk1	127050gf1	35574p1	5082bb1

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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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