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	16	Product of Tamagawa factors cp
deg	5120	Modular degree for the optimal curve
Δ	-28571735808 = -1 · 28 · 32 · 7 · 116	Discriminant
Eigenvalues	2+ 3+ -2 7- 11- -6 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-486,-9324]	[a1,a2,a3,a4,a6]
Generators	[39:162:1]	Generators of the group modulo torsion
j	-7189057/16128	j-invariant
L	2.0115011442453	L(r)(E,1)/r!
Ω	0.47547940177063	Real period
R	1.0576173945468	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	40656co1 15246bs1 127050hk1 35574bg1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5082i1

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 5082i1

-4	-3	5	-7	-11
40656co1	15246bs1	127050hk1	35574bg1	42a1

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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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