Cremona's table of elliptic curves

8330 = 2 · 5 · 7² · 17

Field	Data	Notes
Atkin-Lehner	2- 5- 7- 17+	Signs for the Atkin-Lehner involutions
Class	8330v	Isogeny class
Conductor	8330	Conductor
∏ cp	448	Product of Tamagawa factors cp
deg	129024	Modular degree for the optimal curve
Δ	-1597217316850892800 = -1 · 228 · 52 · 77 · 172	Discriminant
Eigenvalues	2-  0 5- 7- -4 -2 17+  8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-215977,-71986071]	[a1,a2,a3,a4,a6]
j	-9470133471933009/13576123187200	j-invariant
L	2.9477211188622	L(r)(E,1)/r!
Ω	0.10527575424508	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	66640cc1 74970be1 41650r1 1190d1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8330v1

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	-	-	-4	-2	+	8	0	-2	8	-2	-2	4	8	-2	0	-2	4	0	14	8	-16	-10	14

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Quadratic twists for elliptic curve 8330v1

-4	-3	5	-7
66640cc1	74970be1	41650r1	1190d1

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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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