Cremona's table of elliptic curves

192 = 2⁶ · 3

Field	Data	Notes
Atkin-Lehner	2+ 3+	Signs for the Atkin-Lehner involutions
Class	192a	Isogeny class
Conductor	192	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-2654208 = -1 · 215 · 34	Discriminant
Eigenvalues	2+ 3+ -2 -4 -4  2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,31,33]	[a1,a2,a3,a4,a6]
Generators	[1:8:1]	Generators of the group modulo torsion
j	97336/81	j-invariant
L	1.1195591687307	L(r)(E,1)/r!
Ω	1.6566381702366	Real period
R	0.33790093360302	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	192b4 96a4 576c4 4800x4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 192a4

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	-4	-4	2	-6	4	0	-2	4	2	2	-4	8	-10	4	-6	-4	-16	-6	4	-12	10	-14

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Quadratic twists for elliptic curve 192a4

-4	8	-3	5	-7	-11	13	17	-19	-23
192b4	96a4	576c4	4800x4	9408bg4	23232u3	32448e3	55488bj3	69312bv3	101568k3

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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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