Cremona's table of elliptic curves

17080 = 2³ · 5 · 7 · 61

Field	Data	Notes
Atkin-Lehner	2+ 5- 7+ 61-	Signs for the Atkin-Lehner involutions
Class	17080d	Isogeny class
Conductor	17080	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-225057831040000 = -1 · 210 · 54 · 78 · 61	Discriminant
Eigenvalues	2+  0 5- 7+ -4 -2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-18707,-1220994]	[a1,a2,a3,a4,a6]
Generators	[1967:87020:1]	Generators of the group modulo torsion
j	-707027317838244/219783038125	j-invariant
L	4.3223617830876	L(r)(E,1)/r!
Ω	0.20091426896242	Real period
R	5.3783658639698	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	34160i3 85400z3 119560d3	Quadratic twists by: -4 5 -7

Hecke Eigenvalues for elliptic curve 17080d4

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

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Quadratic twists for elliptic curve 17080d4

-4	5	-7
34160i3	85400z3	119560d3

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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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