Cremona's table of elliptic curves

1717 = 17 · 101

Field	Data	Notes
Atkin-Lehner	17- 101-	Signs for the Atkin-Lehner involutions
Class	1717c	Isogeny class
Conductor	1717	Conductor
∏ cp	5	Product of Tamagawa factors cp
deg	1560	Modular degree for the optimal curve
Δ	143405557 = 175 · 101	Discriminant
Eigenvalues	-2 -1 -4  3 -3 -1 17-  5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-600,5832]	[a1,a2,a3,a4,a6]
Generators	[19:30:1]	Generators of the group modulo torsion
j	23927707242496/143405557	j-invariant
L	0.97121388182141	L(r)(E,1)/r!
Ω	1.8458528330605	Real period
R	2.630799878588	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	5	Number of elements in the torsion subgroup
Twists	27472m1 109888i1 15453d1 42925e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1717c1

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	-4	3	-3	-1	-	5	4	-10	-8	8	2	9	8	-6	10	2	-2	12	-11	10	-16	0	-12

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Quadratic twists for elliptic curve 1717c1

-4	8	-3	5	-7	17
27472m1	109888i1	15453d1	42925e1	84133a1	29189d1

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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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