Cremona's table of elliptic curves

60192 = 2⁵ · 3² · 11 · 19

Field	Data	Notes
Atkin-Lehner	2- 3- 11+ 19+	Signs for the Atkin-Lehner involutions
Class	60192q	Isogeny class
Conductor	60192	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	391292301312 = 212 · 37 · 112 · 192	Discriminant
Eigenvalues	2- 3- -2  4 11+ -2  6 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-6290076,6072002656]	[a1,a2,a3,a4,a6]
Generators	[860:36036:1]	Generators of the group modulo torsion
j	9217304063844205888/131043	j-invariant
L	6.6874713283798	L(r)(E,1)/r!
Ω	0.48376345336096	Real period
R	3.4559614217031	Regulator
r	1	Rank of the group of rational points
S	1.0000000000297	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	60192j4 120384bu1 20064i2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 60192q4

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	+	-2	6	+	8	6	-4	6	6	-12	0	6	-12	14	-12	8	-6	-12	-4	-18	-14

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Quadratic twists for elliptic curve 60192q4

-4	8	-3
60192j4	120384bu1	20064i2

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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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