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	1	Product of Tamagawa factors cp
Δ	17 = Prime discriminant	Discriminant
Eigenvalues	-1  0 -2  4  0 -2 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-91,-310]	[a1,a2,a3,a4,a6]
j	82483294977/17	j-invariant
L	0.38676993838778	L(r)(E,1)/r!
Ω	1.5470797535511	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	272b3 1088e3 153c3 425a3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 17a3

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 17a3

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53	-59	61	-67	-71	73	-79	-83
272b3	1088e3	153c3	425a3	833a3	2057c3	2873a3	289a3	6137b3	8993a3	14297a3	16337a3	23273b4	28577a4	31433b4	37553a4	47753f4	59177b4	63257a4	76313b4	85697a4	90593a4	106097a4	117113c4

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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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