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	8664a	Isogeny class
Conductor	8664	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	63212544 = 210 · 32 · 193	Discriminant
Eigenvalues	2+ 3+ -2 -4  2  0 -2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-424,3484]	[a1,a2,a3,a4,a6]
Generators	[-6:76:1]	Generators of the group modulo torsion
j	1203052/9	j-invariant
L	2.5457275187814	L(r)(E,1)/r!
Ω	1.9759719711505	Real period
R	0.64417095888744	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	17328i2 69312bf2 25992v2 8664l2	Quadratic twists by: -4 8 -3 -19

Hecke Eigenvalues for elliptic curve 8664a2

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	-4	2	0	-2	+	6	-6	4	-4	2	-4	6	2	-12	10	16	-8	10	8	-10	18	12

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Quadratic twists for elliptic curve 8664a2

-4	8	-3	-19
17328i2	69312bf2	25992v2	8664l2

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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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