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	8330q	Isogeny class
Conductor	8330	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	4320	Modular degree for the optimal curve
Δ	-4336806250 = -1 · 2 · 55 · 74 · 172	Discriminant
Eigenvalues	2-  0 5+ 7+ -1 -1 17-  1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,407,-269]	[a1,a2,a3,a4,a6]
Generators	[158:903:8]	Generators of the group modulo torsion
j	3112538751/1806250	j-invariant
L	5.6955283646627	L(r)(E,1)/r!
Ω	0.81952338632525	Real period
R	3.4749028884956	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	66640y1 74970bi1 41650a1 8330u1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8330q1

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	+	+	-1	-1	-	1	-3	4	10	7	-7	-2	-5	13	-12	-10	-8	12	-14	-4	-2	-14	-14

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Quadratic twists for elliptic curve 8330q1

-4	-3	5	-7
66640y1	74970bi1	41650a1	8330u1

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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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