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	16170bu	Isogeny class
Conductor	16170	Conductor
∏ cp	192	Product of Tamagawa factors cp
deg	18432	Modular degree for the optimal curve
Δ	-14941080000 = -1 · 26 · 32 · 54 · 73 · 112	Discriminant
Eigenvalues	2- 3+ 5- 7- 11- -4  2  6	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,615,615]	[a1,a2,a3,a4,a6]
Generators	[13:98:1]	Generators of the group modulo torsion
j	74991286313/43560000	j-invariant
L	6.7755333655708	L(r)(E,1)/r!
Ω	0.75043789980918	Real period
R	0.18809943521236	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	129360hr1 48510t1 80850cq1 16170ca1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 16170bu1

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

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Quadratic twists for elliptic curve 16170bu1

-4	-3	5	-7
129360hr1	48510t1	80850cq1	16170ca1

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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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