Cremona's table of elliptic curves

17680 = 2⁴ · 5 · 13 · 17

Field	Data	Notes
Atkin-Lehner	2- 5+ 13- 17+	Signs for the Atkin-Lehner involutions
Class	17680i	Isogeny class
Conductor	17680	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	249488281250000 = 24 · 512 · 13 · 173	Discriminant
Eigenvalues	2-  2 5+  4  0 13- 17+ -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-16081,-191100]	[a1,a2,a3,a4,a6]
Generators	[482390731623243245171424:3041029119277997376484375:3141305093964520194048]	Generators of the group modulo torsion
j	28745501621960704/15593017578125	j-invariant
L	7.5784308681553	L(r)(E,1)/r!
Ω	0.45204624792894	Real period
R	33.529449267087	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	4420a3 70720bj3 88400be3	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 17680i3

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	+	4	0	-	+	-2	-6	-6	4	2	-6	-8	-6	6	-6	2	-2	-12	2	10	-6	-6	2

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Quadratic twists for elliptic curve 17680i3

-4	8	5
4420a3	70720bj3	88400be3

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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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