Cremona's table of elliptic curves

5168 = 2⁴ · 17 · 19

Field	Data	Notes
Atkin-Lehner	2- 17+ 19-	Signs for the Atkin-Lehner involutions
Class	5168h	Isogeny class
Conductor	5168	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	10752	Modular degree for the optimal curve
Δ	36298047488 = 214 · 17 · 194	Discriminant
Eigenvalues	2-  2  4 -4 -2 -6 17+ 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-3856,-90432]	[a1,a2,a3,a4,a6]
Generators	[-906:190:27]	Generators of the group modulo torsion
j	1548415333009/8861828	j-invariant
L	5.6572396919573	L(r)(E,1)/r!
Ω	0.60604599909986	Real period
R	2.333667617788	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	646c1 20672x1 46512bs1 129200ck1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5168h1

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

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Quadratic twists for elliptic curve 5168h1

-4	8	-3	5	17	-19
646c1	20672x1	46512bs1	129200ck1	87856t1	98192r1

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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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