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	17040z	Isogeny class
Conductor	17040	Conductor
∏ cp	192	Product of Tamagawa factors cp
Δ	3793943643955200 = 213 · 36 · 52 · 714	Discriminant
Eigenvalues	2- 3- 5-  0  0 -6 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-3112080,2112081300]	[a1,a2,a3,a4,a6]
Generators	[735:14910:1]	Generators of the group modulo torsion
j	813797144010554645521/926255772450	j-invariant
L	6.2575187155791	L(r)(E,1)/r!
Ω	0.37255813343043	Real period
R	1.3996738929397	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	2130j3 68160ca4 51120t4 85200bx4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 17040z4

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	0	-6	-6	4	8	6	0	-2	-6	-4	0	-6	-8	10	0	-	-6	-8	-4	-6	2

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Quadratic twists for elliptic curve 17040z4

-4	8	-3	5
2130j3	68160ca4	51120t4	85200bx4

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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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