Cremona's table of elliptic curves

8118 = 2 · 3² · 11 · 41

Field	Data	Notes
Atkin-Lehner	2- 3- 11- 41-	Signs for the Atkin-Lehner involutions
Class	8118q	Isogeny class
Conductor	8118	Conductor
∏ cp	288	Product of Tamagawa factors cp
Δ	-93034882787185152 = -1 · 29 · 312 · 112 · 414	Discriminant
Eigenvalues	2- 3-  0 -2 11-  0 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-69035,16268411]	[a1,a2,a3,a4,a6]
Generators	[-3:4060:1]	Generators of the group modulo torsion
j	-49911230110731625/127619866649088	j-invariant
L	6.0973005807728	L(r)(E,1)/r!
Ω	0.29913558488482	Real period
R	0.28309814869107	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	64944bd2 2706d2 89298n2	Quadratic twists by: -4 -3 -11

Hecke Eigenvalues for elliptic curve 8118q2

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	-	0	-2	4	2	-10	0	-2	-	0	-6	-4	0	0	12	-2	-6	10	-12	-10	-2

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Quadratic twists for elliptic curve 8118q2

-4	-3	-11
64944bd2	2706d2	89298n2

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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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