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	17040p	Isogeny class
Conductor	17040	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	34744320	Modular degree for the optimal curve
Δ	-1.2374013943584E+29	Discriminant
Eigenvalues	2- 3+ 5- -2  6  2  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-14315160160,659460282976000]	[a1,a2,a3,a4,a6]
j	-79204963502810190656794906124641/30209994979453807519334400	j-invariant
L	2.0778066229688	L(r)(E,1)/r!
Ω	0.032465728483888	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	16	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2130n1 68160da1 51120x1 85200de1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 17040p1

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

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Quadratic twists for elliptic curve 17040p1

-4	8	-3	5
2130n1	68160da1	51120x1	85200de1

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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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