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	8568a	Isogeny class
Conductor	8568	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	5376	Modular degree for the optimal curve
Δ	-14688242352 = -1 · 24 · 33 · 76 · 172	Discriminant
Eigenvalues	2+ 3+  2 7+ -6  2 17+  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-54,5833]	[a1,a2,a3,a4,a6]
Generators	[-16:51:1]	Generators of the group modulo torsion
j	-40310784/34000561	j-invariant
L	4.5670315888812	L(r)(E,1)/r!
Ω	1.0084531795321	Real period
R	1.1321873145861	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	17136a1 68544e1 8568h1 59976f1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 8568a1

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	+	-6	2	+	0	6	4	-4	-6	-6	4	12	4	-4	2	4	-14	10	-16	-8	10	2

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Quadratic twists for elliptic curve 8568a1

-4	8	-3	-7
17136a1	68544e1	8568h1	59976f1

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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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