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	17556h	Isogeny class
Conductor	17556	Conductor
∏ cp	720	Product of Tamagawa factors cp
deg	472320	Modular degree for the optimal curve
Δ	-3.6763507982205E+19	Discriminant
Eigenvalues	2- 3+ -2 7- 11- -4  6 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-492689,-320489406]	[a1,a2,a3,a4,a6]
Generators	[995:13167:1]	Generators of the group modulo torsion
j	-826652929853217390592/2297719248887827611	j-invariant
L	3.6247035241807	L(r)(E,1)/r!
Ω	0.083556860172958	Real period
R	0.24100046075596	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	70224cf1 52668v1 122892bf1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 17556h1

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

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Quadratic twists for elliptic curve 17556h1

-4	-3	-7
70224cf1	52668v1	122892bf1

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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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