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	8664j	Isogeny class
Conductor	8664	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	864	Modular degree for the optimal curve
Δ	-155952 = -1 · 24 · 33 · 192	Discriminant
Eigenvalues	2- 3+  2 -3  0 -5 -4 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,13,-12]	[a1,a2,a3,a4,a6]
Generators	[1:1:1]	Generators of the group modulo torsion
j	38912/27	j-invariant
L	3.5726184943291	L(r)(E,1)/r!
Ω	1.8325339121648	Real period
R	0.97477554729361	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	17328n1 69312bu1 25992l1 8664e1	Quadratic twists by: -4 8 -3 -19

Hecke Eigenvalues for elliptic curve 8664j1

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	-3	0	-5	-4	-	6	4	7	1	0	11	6	2	-8	7	-3	-6	9	-5	16	-12	14

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Quadratic twists for elliptic curve 8664j1

-4	8	-3	-19
17328n1	69312bu1	25992l1	8664e1

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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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