Cremona's table of elliptic curves

17556 = 2² · 3 · 7 · 11 · 19

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 11+ 19-	Signs for the Atkin-Lehner involutions
Class	17556m	Isogeny class
Conductor	17556	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	-2356443120337152 = -1 · 28 · 3 · 72 · 113 · 196	Discriminant
Eigenvalues	2- 3-  0 7- 11+  2  6 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,5292,-2329068]	[a1,a2,a3,a4,a6]
Generators	[134210:903669:1000]	Generators of the group modulo torsion
j	64011968750000/9204855938817	j-invariant
L	6.557344939087	L(r)(E,1)/r!
Ω	0.21735609673688	Real period
R	10.056224229166	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	70224bh4 52668ba4 122892b4	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 17556m4

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

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Quadratic twists for elliptic curve 17556m4

-4	-3	-7
70224bh4	52668ba4	122892b4

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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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