Cremona's table of elliptic curves

192 = 2⁶ · 3

Field	Data	Notes
Atkin-Lehner	2+ 3-	Signs for the Atkin-Lehner involutions
Class	192c	Isogeny class
Conductor	192	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	5308416 = 216 · 34	Discriminant
Eigenvalues	2+ 3-  2  0 -4  2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-97,-385]	[a1,a2,a3,a4,a6]
j	1556068/81	j-invariant
L	1.5248868380819	L(r)(E,1)/r!
Ω	1.5248868380819	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	192d4 24a2 576d4 4800c3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 192c3

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 192c3

-4	8	-3	5	-7	-11	13	17	-19	-23
192d4	24a2	576d4	4800c3	9408q4	23232bw3	32448bh3	55488k3	69312p3	101568bg3

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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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