Cremona's table of elliptic curves

8993 = 17 · 23²

Field	Data	Notes
Atkin-Lehner	17+ 23-	Signs for the Atkin-Lehner involutions
Class	8993a	Isogeny class
Conductor	8993	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	42782371921 = 172 · 236	Discriminant
Eigenvalues	-1  0  2 -4  0 -2 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-3009,63488]	[a1,a2,a3,a4,a6]
j	20346417/289	j-invariant
L	0.57252618336207	L(r)(E,1)/r!
Ω	1.1450523667241	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	80937s2 17a2	Quadratic twists by: -3 -23

Hecke Eigenvalues for elliptic curve 8993a2

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
-1	0	2	-4	0	-2	+	4	-	6	4	2	-6	-4	0	-6	-12	10	-4	-4	-6	-12	4	-10	-2

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Quadratic twists for elliptic curve 8993a2

-3	-23
80937s2	17a2

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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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