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	5082w	Isogeny class
Conductor	5082	Conductor
∏ cp	13	Product of Tamagawa factors cp
deg	65520	Modular degree for the optimal curve
Δ	-72580457782812672 = -1 · 213 · 321 · 7 · 112	Discriminant
Eigenvalues	2- 3+  2 7- 11- -5  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,54288,12035409]	[a1,a2,a3,a4,a6]
j	146234339790153527/599838494072832	j-invariant
L	3.2066528303095	L(r)(E,1)/r!
Ω	0.2466656023315	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	40656cn1 15246t1 127050db1 35574dg1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5082w1

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	-	-	-5	6	-4	1	1	-1	12	9	-5	10	-2	13	11	-7	-1	-4	-4	11	13	-12

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Quadratic twists for elliptic curve 5082w1

-4	-3	5	-7	-11
40656cn1	15246t1	127050db1	35574dg1	5082c1

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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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