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	8330r	Isogeny class
Conductor	8330	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	28224	Modular degree for the optimal curve
Δ	-163270693922000 = -1 · 24 · 53 · 710 · 172	Discriminant
Eigenvalues	2-  1 5+ 7- -2 -4 17-  6	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,9554,499540]	[a1,a2,a3,a4,a6]
j	341425679/578000	j-invariant
L	3.1440034104901	L(r)(E,1)/r!
Ω	0.39300042631126	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	66640bo1 74970br1 41650j1 8330t1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8330r1

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
-	1	+	-	-2	-4	-	6	1	1	6	2	5	9	-12	-4	8	15	-11	-6	-4	6	-7	15	12

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Quadratic twists for elliptic curve 8330r1

-4	-3	5	-7
66640bo1	74970br1	41650j1	8330t1

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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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