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,-1,0]	[a1,a2,a3,a4,a6]
j	35937/17	j-invariant
L	0.38676993838778	L(r)(E,1)/r!
Ω	6.1883190142045	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	272b1 1088e1 153c1 425a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 17a4

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 17a4

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53	-59	61	-67	-71	73	-79	-83
272b1	1088e1	153c1	425a1	833a1	2057c1	2873a1	289a1	6137b1	8993a1	14297a1	16337a1	23273b1	28577a1	31433b1	37553a1	47753f1	59177b1	63257a1	76313b1	85697a1	90593a1	106097a1	117113c1

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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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