Cremona's table of elliptic curves

17040 = 2⁴ · 3 · 5 · 71

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 71+	Signs for the Atkin-Lehner involutions
Class	17040t	Isogeny class
Conductor	17040	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	21504	Modular degree for the optimal curve
Δ	-1072064102400 = -1 · 226 · 32 · 52 · 71	Discriminant
Eigenvalues	2- 3- 5+  2 -2  0  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1456,-54700]	[a1,a2,a3,a4,a6]
Generators	[292:4950:1]	Generators of the group modulo torsion
j	-83396175409/261734400	j-invariant
L	6.0863670407434	L(r)(E,1)/r!
Ω	0.35649258140245	Real period
R	4.2682283995922	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	2130i1 68160cj1 51120bp1 85200bs1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 17040t1

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	-2	0	0	4	4	-2	2	-2	-12	-12	-8	-2	14	-12	-8	+	-14	16	0	-2	-14

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Quadratic twists for elliptic curve 17040t1

-4	8	-3	5
2130i1	68160cj1	51120bp1	85200bs1

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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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