Cremona's table of elliptic curves

192 = 2⁶ · 3

Field	Data	Notes
Atkin-Lehner	2- 3+	Signs for the Atkin-Lehner involutions
Class	192d	Isogeny class
Conductor	192	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	1179648 = 217 · 32	Discriminant
Eigenvalues	2- 3+  2  0  4  2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1537,23713]	[a1,a2,a3,a4,a6]
j	3065617154/9	j-invariant
L	1.1920055072756	L(r)(E,1)/r!
Ω	2.3840110145512	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	192c5 48a5 576i5 4800cb5	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 192d5

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

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Quadratic twists for elliptic curve 192d5

-4	8	-3	5	-7	-11	13	17	-19	-23
192c5	48a5	576i5	4800cb5	9408cz5	23232cz6	32448ci6	55488du6	69312dl6	101568cm6

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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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