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	2	Product of Tamagawa factors cp
deg	8	Modular degree for the optimal curve
Δ	-3072 = -1 · 210 · 3	Discriminant
Eigenvalues	2+ 3-  2  0 -4  2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,3,3]	[a1,a2,a3,a4,a6]
j	2048/3	j-invariant
L	1.5248868380819	L(r)(E,1)/r!
Ω	3.0497736761638	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	192d1 24a4 576d1 4800c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 192c1

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 192c1

-4	8	-3	5	-7	-11	13	17	-19	-23
192d1	24a4	576d1	4800c1	9408q1	23232bw1	32448bh1	55488k1	69312p1	101568bg1

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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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