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	17040g	Isogeny class
Conductor	17040	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	-2981318400 = -1 · 28 · 38 · 52 · 71	Discriminant
Eigenvalues	2+ 3- 5+  2  0  0  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,244,-2100]	[a1,a2,a3,a4,a6]
Generators	[22:120:1]	Generators of the group modulo torsion
j	6249886256/11645775	j-invariant
L	6.1888950106716	L(r)(E,1)/r!
Ω	0.74602122139587	Real period
R	1.036983740069	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	8520b2 68160cs2 51120f2 85200i2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 17040g2

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	0	0	0	4	-2	2	-8	-6	-2	-8	6	0	-8	-6	-14	-	10	8	-12	-14	-4

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Quadratic twists for elliptic curve 17040g2

-4	8	-3	5
8520b2	68160cs2	51120f2	85200i2

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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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