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	17040a	Isogeny class
Conductor	17040	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	77429760 = 210 · 3 · 5 · 712	Discriminant
Eigenvalues	2+ 3+ 5+  4  0 -4  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-296,2016]	[a1,a2,a3,a4,a6]
Generators	[13:14:1]	Generators of the group modulo torsion
j	2810381476/75615	j-invariant
L	4.5883548720307	L(r)(E,1)/r!
Ω	1.926607614912	Real period
R	2.3815720629965	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	8520i2 68160dh2 51120m2 85200w2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 17040a2

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
+	+	+	4	0	-4	6	4	-6	6	2	-6	4	-12	-10	-6	4	-6	-4	+	-14	8	4	-2	-16

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Quadratic twists for elliptic curve 17040a2

-4	8	-3	5
8520i2	68160dh2	51120m2	85200w2

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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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