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	4	Product of Tamagawa factors cp
deg	1	Modular degree for the optimal curve
Δ	-83521 = -1 · 174	Discriminant
Eigenvalues	-1  0 -2  4  0 -2 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-1,-14]	[a1,a2,a3,a4,a6]
j	-35937/83521	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	4	Number of elements in the torsion subgroup
Twists	272b4 1088e4 153c4 425a4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 17a1

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 17a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53	-59	61	-67	-71	73	-79	-83
272b4	1088e4	153c4	425a4	833a4	2057c4	2873a4	289a4	6137b4	8993a4	14297a4	16337a4	23273b3	28577a3	31433b3	37553a3	47753f3	59177b3	63257a3	76313b3	85697a3	90593a3	106097a3	117113c3

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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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