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	8664g	Isogeny class
Conductor	8664	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	3456	Modular degree for the optimal curve
Δ	-2258202288 = -1 · 24 · 3 · 196	Discriminant
Eigenvalues	2+ 3- -2  0  4  2  2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,241,-1698]	[a1,a2,a3,a4,a6]
Generators	[1587:12635:27]	Generators of the group modulo torsion
j	2048/3	j-invariant
L	4.8345148647268	L(r)(E,1)/r!
Ω	0.77347530954378	Real period
R	3.1251901677238	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	17328f1 69312p1 25992bc1 24a4	Quadratic twists by: -4 8 -3 -19

Hecke Eigenvalues for elliptic curve 8664g1

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	4	2	2	-	-8	-6	-8	-6	6	4	0	2	-4	-2	4	-8	10	8	-4	6	-2

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Quadratic twists for elliptic curve 8664g1

-4	8	-3	-19
17328f1	69312p1	25992bc1	24a4

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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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