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	8330w	Isogeny class
Conductor	8330	Conductor
∏ cp	10	Product of Tamagawa factors cp
deg	11520	Modular degree for the optimal curve
Δ	-15680258720 = -1 · 25 · 5 · 78 · 17	Discriminant
Eigenvalues	2-  3 5- 7-  2  1 17+ -1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,603,1789]	[a1,a2,a3,a4,a6]
j	206425071/133280	j-invariant
L	7.7480139530475	L(r)(E,1)/r!
Ω	0.77480139530475	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	66640ci1 74970ba1 41650t1 1190e1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8330w1

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
-	3	-	-	2	1	+	-1	-6	1	5	-2	10	-8	11	7	-9	7	-8	-3	-7	-4	14	11	11

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Quadratic twists for elliptic curve 8330w1

-4	-3	5	-7
66640ci1	74970ba1	41650t1	1190e1

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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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