Cremona's table of elliptic curves

1717 = 17 · 101

Field	Data	Notes
Atkin-Lehner	17+ 101-	Signs for the Atkin-Lehner involutions
Class	1717a	Isogeny class
Conductor	1717	Conductor
∏ cp	1	Product of Tamagawa factors cp
Δ	496213 = 173 · 101	Discriminant
Eigenvalues	0  1  0  5  3 -1 17+  5	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-7163,-235745]	[a1,a2,a3,a4,a6]
j	40650809135104000/496213	j-invariant
L	2.0757772894263	L(r)(E,1)/r!
Ω	0.51894432235658	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	27472j2 109888a2 15453f2 42925g2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1717a2

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
0	1	0	5	3	-1	+	5	6	-6	-4	2	6	5	0	12	0	2	-10	12	11	-10	0	-6	14

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Quadratic twists for elliptic curve 1717a2

-4	8	-3	5	-7	17
27472j2	109888a2	15453f2	42925g2	84133c2	29189c2

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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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