Cremona's table of elliptic curves

8568 = 2³ · 3² · 7 · 17

Field	Data	Notes
Atkin-Lehner	2+ 3- 7+ 17+	Signs for the Atkin-Lehner involutions
Class	8568d	Isogeny class
Conductor	8568	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	5120	Modular degree for the optimal curve
Δ	-466373376 = -1 · 28 · 37 · 72 · 17	Discriminant
Eigenvalues	2+ 3- -3 7+ -5 -3 17+ -5	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-804,8836]	[a1,a2,a3,a4,a6]
Generators	[-22:126:1] [-10:126:1]	Generators of the group modulo torsion
j	-307981312/2499	j-invariant
L	4.8528216672135	L(r)(E,1)/r!
Ω	1.672691807847	Real period
R	0.090662653089499	Regulator
r	2	Rank of the group of rational points
S	0.99999999999962	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	17136k1 68544bh1 2856i1 59976u1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 8568d1

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
+	-	-3	+	-5	-3	+	-5	-5	-2	8	-6	-9	-1	0	-4	-12	-6	-16	-8	-10	8	-14	8	-8

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Quadratic twists for elliptic curve 8568d1

-4	8	-3	-7
17136k1	68544bh1	2856i1	59976u1

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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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