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	17220k	Isogeny class
Conductor	17220	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	24938047265250000 = 24 · 3 · 56 · 7 · 416	Discriminant
Eigenvalues	2- 3- 5+ 7-  0 -4  6  8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-86401,6121724]	[a1,a2,a3,a4,a6]
j	4458256618527145984/1558627954078125	j-invariant
L	3.1214192287036	L(r)(E,1)/r!
Ω	0.34682435874484	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	9	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	68880be3 51660s3 86100a3 120540t3	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 17220k3

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	6	8	6	0	2	2	+	8	0	12	0	-10	-4	0	2	-16	0	-18	8

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Quadratic twists for elliptic curve 17220k3

-4	-3	5	-7
68880be3	51660s3	86100a3	120540t3

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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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