Cremona's table of elliptic curves

13566 = 2 · 3 · 7 · 17 · 19

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 17+ 19-	Signs for the Atkin-Lehner involutions
Class	13566t	Isogeny class
Conductor	13566	Conductor
∏ cp	162	Product of Tamagawa factors cp
deg	46656	Modular degree for the optimal curve
Δ	-76015542235752 = -1 · 23 · 36 · 79 · 17 · 19	Discriminant
Eigenvalues	2- 3-  0 7-  0 -4 17+ 19-	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-20853,-1234359]	[a1,a2,a3,a4,a6]
Generators	[168:21:1]	Generators of the group modulo torsion
j	-1002837679918908625/76015542235752	j-invariant
L	8.6317420704863	L(r)(E,1)/r!
Ω	0.19778374851952	Real period
R	2.4245734532168	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	108528n1 40698p1 94962bn1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 13566t1

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	-	0	-4	+	-	-3	-6	-7	2	12	-1	-3	-9	-9	-4	8	-6	-1	-10	-6	15	8

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Quadratic twists for elliptic curve 13566t1

-4	-3	-7
108528n1	40698p1	94962bn1

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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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