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	8330k	Isogeny class
Conductor	8330	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	524296650752000000 = 224 · 56 · 76 · 17	Discriminant
Eigenvalues	2+  2 5- 7-  6 -2 17+ -8	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-204257,6903989]	[a1,a2,a3,a4,a6]
Generators	[-407:4981:1]	Generators of the group modulo torsion
j	8010684753304969/4456448000000	j-invariant
L	4.8531115488068	L(r)(E,1)/r!
Ω	0.25384354738601	Real period
R	3.1864190881762	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	66640cg3 74970dd3 41650cf3 170b3	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8330k3

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
+	2	-	-	6	-2	+	-8	-6	-6	-2	2	6	-4	-12	6	0	-2	8	-6	-2	-10	-12	-6	-2

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Quadratic twists for elliptic curve 8330k3

-4	-3	5	-7
66640cg3	74970dd3	41650cf3	170b3

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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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