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	3	Product of Tamagawa factors cp
deg	328	Modular degree for the optimal curve
Δ	17515117 = 17 · 1013	Discriminant
Eigenvalues	0  1  0  5  3 -1 17+  5	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-93,-314]	[a1,a2,a3,a4,a6]
j	89915392000/17515117	j-invariant
L	2.0757772894263	L(r)(E,1)/r!
Ω	1.5568329670698	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	27472j1 109888a1 15453f1 42925g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1717a1

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 1717a1

-4	8	-3	5	-7	17
27472j1	109888a1	15453f1	42925g1	84133c1	29189c1

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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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