Cremona's table of elliptic curves

17 = Prime conductor

Field	Data	Notes
Atkin-Lehner	17-	Signs for the Atkin-Lehner involutions
Class	17a	Isogeny class
Conductor	17	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	289 = 172	Discriminant
Eigenvalues	-1  0 -2  4  0 -2 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-6,-4]	[a1,a2,a3,a4,a6]
j	20346417/289	j-invariant
L	0.38676993838778	L(r)(E,1)/r!
Ω	3.0941595071022	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	272b2 1088e2 153c2 425a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 17a2

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	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 17a2

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53	-59	61	-67	-71	73	-79	-83
272b2	1088e2	153c2	425a2	833a2	2057c2	2873a2	289a2	6137b2	8993a2	14297a2	16337a2	23273b2	28577a2	31433b2	37553a2	47753f2	59177b2	63257a2	76313b2	85697a2	90593a2	106097a2	117113c2

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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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