Cremona's table of elliptic curves

16008 = 2³ · 3 · 23 · 29

Field	Data	Notes
Atkin-Lehner	2+ 3+ 23+ 29+	Signs for the Atkin-Lehner involutions
Class	16008a	Isogeny class
Conductor	16008	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	20736	Modular degree for the optimal curve
Δ	-1909620188928 = -1 · 28 · 36 · 233 · 292	Discriminant
Eigenvalues	2+ 3+  0  2 -6 -2  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,3012,18324]	[a1,a2,a3,a4,a6]
Generators	[426:8856:1]	Generators of the group modulo torsion
j	11800609886000/7459453863	j-invariant
L	3.9041202461732	L(r)(E,1)/r!
Ω	0.51692892487333	Real period
R	3.7762640648614	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	32016g1 128064bc1 48024k1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 16008a1

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

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Quadratic twists for elliptic curve 16008a1

-4	8	-3
32016g1	128064bc1	48024k1

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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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