Cremona's table of elliptic curves

16170 = 2 · 3 · 5 · 7² · 11

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 7- 11+	Signs for the Atkin-Lehner involutions
Class	16170t	Isogeny class
Conductor	16170	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	24576	Modular degree for the optimal curve
Δ	104359368960 = 28 · 32 · 5 · 77 · 11	Discriminant
Eigenvalues	2+ 3- 5+ 7- 11+  2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-3799,88442]	[a1,a2,a3,a4,a6]
Generators	[55:188:1]	Generators of the group modulo torsion
j	51520374361/887040	j-invariant
L	4.1414817099865	L(r)(E,1)/r!
Ω	1.06156667993	Real period
R	1.9506460537456	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	129360ee1 48510ee1 80850dx1 2310d1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 16170t1

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	-2	4	4	-10	4	-10	-6	4	0	-2	0	14	0	0	-2	-8	-4	-18	-2

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Quadratic twists for elliptic curve 16170t1

-4	-3	5	-7
129360ee1	48510ee1	80850dx1	2310d1

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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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