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	1	Product of Tamagawa factors cp
deg	8	Modular degree for the optimal curve
Δ	192 = 26 · 3	Discriminant
Eigenvalues	2+ 3+ -2 -4 -4  2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-4,-2]	[a1,a2,a3,a4,a6]
Generators	[3:2:1]	Generators of the group modulo torsion
j	140608/3	j-invariant
L	1.1195591687307	L(r)(E,1)/r!
Ω	3.3132763404732	Real period
R	1.3516037344121	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	192b1 96a2 576c1 4800x1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 192a1

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 192a1

-4	8	-3	5	-7	-11	13	17	-19	-23
192b1	96a2	576c1	4800x1	9408bg1	23232u1	32448e1	55488bj1	69312bv1	101568k1

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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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