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	5082r	Isogeny class
Conductor	5082	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	378129066084 = 22 · 32 · 72 · 118	Discriminant
Eigenvalues	2- 3+ -2 7+ 11- -2  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-1999,16721]	[a1,a2,a3,a4,a6]
Generators	[7:52:1]	Generators of the group modulo torsion
j	498677257/213444	j-invariant
L	4.1902654906966	L(r)(E,1)/r!
Ω	0.85940246292775	Real period
R	2.4378947416683	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	40656dj2 15246l2 127050dk2 35574dd2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5082r2

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

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Quadratic twists for elliptic curve 5082r2

-4	-3	5	-7	-11
40656dj2	15246l2	127050dk2	35574dd2	462c2

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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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