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	4	Product of Tamagawa factors cp
Δ	-859963392 = -1 · 217 · 38	Discriminant
Eigenvalues	2- 3+  2  0  4  2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,63,1377]	[a1,a2,a3,a4,a6]
j	207646/6561	j-invariant
L	1.1920055072756	L(r)(E,1)/r!
Ω	1.1920055072756	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	192c6 48a6 576i6 4800cb6	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 192d6

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 192d6

-4	8	-3	5	-7	-11	13	17	-19	-23
192c6	48a6	576i6	4800cb6	9408cz6	23232cz5	32448ci5	55488du5	69312dl5	101568cm5

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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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