Cremona's table of elliptic curves

6192 = 2⁴ · 3² · 43

Field	Data	Notes
Atkin-Lehner	2+ 3+ 43-	Signs for the Atkin-Lehner involutions
Class	6192d	Isogeny class
Conductor	6192	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	102242304 = 211 · 33 · 432	Discriminant
Eigenvalues	2+ 3+ -2 -2 -6 -6  0 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-171,-710]	[a1,a2,a3,a4,a6]
Generators	[-9:10:1] [-7:12:1]	Generators of the group modulo torsion
j	10000422/1849	j-invariant
L	4.4631833499176	L(r)(E,1)/r!
Ω	1.3370832957436	Real period
R	0.83449987074976	Regulator
r	2	Rank of the group of rational points
S	0.99999999999974	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3096f2 24768bn2 6192c2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 6192d2

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

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Quadratic twists for elliptic curve 6192d2

-4	8	-3
3096f2	24768bn2	6192c2

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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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