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	5082t	Isogeny class
Conductor	5082	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	12529822235238 = 2 · 38 · 72 · 117	Discriminant
Eigenvalues	2- 3+  0 7- 11-  2  4 -6	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-12768,523227]	[a1,a2,a3,a4,a6]
j	129938649625/7072758	j-invariant
L	2.8048269586427	L(r)(E,1)/r!
Ω	0.70120673966067	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	40656cf2 15246o2 127050ct2 35574cx2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5082t2

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
-	+	0	-	-	2	4	-6	-4	10	6	-6	12	8	2	6	-8	-6	-4	0	12	0	-14	10	10

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Quadratic twists for elliptic curve 5082t2

-4	-3	5	-7	-11
40656cf2	15246o2	127050ct2	35574cx2	462a2

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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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