Cremona's table of elliptic curves

192 = 2⁶ · 3

Field	Data	Notes
Atkin-Lehner	2+ 3-	Signs for the Atkin-Lehner involutions
Class	192b	Isogeny class
Conductor	192	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	36864 = 212 · 32	Discriminant
Eigenvalues	2+ 3- -2  4  4  2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-9,-9]	[a1,a2,a3,a4,a6]
j	21952/9	j-invariant
L	1.415737208426	L(r)(E,1)/r!
Ω	2.8314744168519	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	192a2 96b1 576b2 4800h2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 192b2

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 192b2

-4	8	-3	5	-7	-11	13	17	-19	-23
192a2	96b1	576b2	4800h2	9408k2	23232ch2	32448bg2	55488j2	69312u2	101568be2

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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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