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	17040s	Isogeny class
Conductor	17040	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	-588902400 = -1 · 212 · 34 · 52 · 71	Discriminant
Eigenvalues	2- 3- 5+  2  0  0  4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-216,1620]	[a1,a2,a3,a4,a6]
Generators	[6:24:1]	Generators of the group modulo torsion
j	-273359449/143775	j-invariant
L	6.0972564499597	L(r)(E,1)/r!
Ω	1.5182577940362	Real period
R	0.50199449608541	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	1065a1 68160ci1 51120bo1 85200br1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 17040s1

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	4	-4	-6	-6	-4	10	2	8	-6	4	0	-14	-14	+	2	-16	4	-6	4

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Quadratic twists for elliptic curve 17040s1

-4	8	-3	5
1065a1	68160ci1	51120bo1	85200br1

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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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