Cremona's table of elliptic curves

3192 = 2³ · 3 · 7 · 19

Field	Data	Notes
Atkin-Lehner	2+ 3- 7- 19+	Signs for the Atkin-Lehner involutions
Class	3192i	Isogeny class
Conductor	3192	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	8407268352 = 210 · 32 · 7 · 194	Discriminant
Eigenvalues	2+ 3- -2 7- -4  2  2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1464,-21600]	[a1,a2,a3,a4,a6]
Generators	[-21:18:1]	Generators of the group modulo torsion
j	339112345828/8210223	j-invariant
L	3.6560119491348	L(r)(E,1)/r!
Ω	0.77291252548867	Real period
R	2.3650877871485	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	6384c4 25536u3 9576z4 79800z3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3192i3

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	2	2	+	0	-2	-8	-2	-2	4	0	-2	-12	14	8	-12	-14	-4	-4	-18	-10

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Quadratic twists for elliptic curve 3192i3

-4	8	-3	5	-7	-19
6384c4	25536u3	9576z4	79800z3	22344i3	60648ba3

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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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