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
Δ	178671708517 = 17 · 1015	Discriminant
Eigenvalues	-2 -1 -4  3 -3 -1 17-  5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-27970,-1791068]	[a1,a2,a3,a4,a6]
Generators	[334:5100:1]	Generators of the group modulo torsion
j	2420007089713278976/178671708517	j-invariant
L	0.97121388182141	L(r)(E,1)/r!
Ω	0.36917056661211	Real period
R	0.52615997571761	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	27472m2 109888i2 15453d2 42925e2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1717c2

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 1717c2

-4	8	-3	5	-7	17
27472m2	109888i2	15453d2	42925e2	84133a2	29189d2

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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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