Cremona's table of elliptic curves

17220 = 2² · 3 · 5 · 7 · 41

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 7+ 41-	Signs for the Atkin-Lehner involutions
Class	17220b	Isogeny class
Conductor	17220	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-14947841025895680 = -1 · 28 · 310 · 5 · 76 · 412	Discriminant
Eigenvalues	2- 3+ 5+ 7+ -2 -4 -2 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,17044,-5825304]	[a1,a2,a3,a4,a6]
Generators	[79710:1536229:216]	Generators of the group modulo torsion
j	2138813134097456/58390004007405	j-invariant
L	3.0212823226418	L(r)(E,1)/r!
Ω	0.19052039462722	Real period
R	7.9290259936564	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	68880cl2 51660k2 86100bf2 120540bj2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 17220b2

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

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Quadratic twists for elliptic curve 17220b2

-4	-3	5	-7
68880cl2	51660k2	86100bf2	120540bj2

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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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