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	147456 = 214 · 32	Discriminant
Eigenvalues	2- 3+  2  0  4  2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-17,-15]	[a1,a2,a3,a4,a6]
j	35152/9	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	192c2 48a1 576i2 4800cb2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 192d2

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 192d2

-4	8	-3	5	-7	-11	13	17	-19	-23
192c2	48a1	576i2	4800cb2	9408cz2	23232cz2	32448ci2	55488du2	69312dl2	101568cm2

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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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