Cremona's table of elliptic curves

1717 = 17 · 101

Field	Data	Notes
Atkin-Lehner	17- 101+	Signs for the Atkin-Lehner involutions
Class	1717b	Isogeny class
Conductor	1717	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	104	Modular degree for the optimal curve
Δ	1717 = 17 · 101	Discriminant
Eigenvalues	-2 -1 -2 -1 -3 -5 17- -3	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-4,4]	[a1,a2,a3,a4,a6]
Generators	[-1:2:1] [1:0:1]	Generators of the group modulo torsion
j	8998912/1717	j-invariant
L	1.5015109202792	L(r)(E,1)/r!
Ω	4.4829106707263	Real period
R	0.33494107524472	Regulator
r	2	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	27472k1 109888k1 15453e1 42925b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1717b1

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
-2	-1	-2	-1	-3	-5	-	-3	-6	-2	2	-8	2	-7	-12	8	-12	-6	12	-4	-11	-6	14	-6	-8

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Quadratic twists for elliptic curve 1717b1

-4	8	-3	5	-7	17
27472k1	109888k1	15453e1	42925b1	84133b1	29189b1

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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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