Cremona's table of elliptic curves

8664 = 2³ · 3 · 19²

Field	Data	Notes
Atkin-Lehner	2- 3+ 19-	Signs for the Atkin-Lehner involutions
Class	8664i	Isogeny class
Conductor	8664	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	17280	Modular degree for the optimal curve
Δ	6178441459968 = 28 · 33 · 197	Discriminant
Eigenvalues	2- 3+  2  0  0 -2  2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-62212,5992132]	[a1,a2,a3,a4,a6]
Generators	[12021:1317650:1]	Generators of the group modulo torsion
j	2211014608/513	j-invariant
L	4.1975971965481	L(r)(E,1)/r!
Ω	0.73497726214299	Real period
R	5.7111932746179	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	17328m1 69312bt1 25992k1 456b1	Quadratic twists by: -4 8 -3 -19

Hecke Eigenvalues for elliptic curve 8664i1

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	0	0	-2	2	-	0	-2	4	-2	-6	-4	0	-10	4	-2	12	0	-6	4	-8	-6	14

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Quadratic twists for elliptic curve 8664i1

-4	8	-3	-19
17328m1	69312bt1	25992k1	456b1

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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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