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	5082l	Isogeny class
Conductor	5082	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	2695303983046752 = 25 · 36 · 72 · 119	Discriminant
Eigenvalues	2+ 3- -2 7- 11+  6  0 -8	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-221917,-40178536]	[a1,a2,a3,a4,a6]
Generators	[-278:359:1]	Generators of the group modulo torsion
j	512576216027/1143072	j-invariant
L	3.1722938736051	L(r)(E,1)/r!
Ω	0.21999374765695	Real period
R	2.4033212363167	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	40656be2 15246bn2 127050ex2 35574g2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5082l2

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 5082l2

-4	-3	5	-7	-11
40656be2	15246bn2	127050ex2	35574g2	5082y2

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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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