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	3192n	Isogeny class
Conductor	3192	Conductor
∏ cp	1	Product of Tamagawa factors cp
Δ	817152 = 211 · 3 · 7 · 19	Discriminant
Eigenvalues	2- 3+ -2 7-  0 -2  6 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-17024,-849300]	[a1,a2,a3,a4,a6]
Generators	[501:10776:1]	Generators of the group modulo torsion
j	266442869452034/399	j-invariant
L	2.6565806712763	L(r)(E,1)/r!
Ω	0.41795740703053	Real period
R	6.3561038196464	Regulator
r	1	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	6384i3 25536bp4 9576l3 79800i4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3192n3

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

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Quadratic twists for elliptic curve 3192n3

-4	8	-3	5	-7	-19
6384i3	25536bp4	9576l3	79800i4	22344bi4	60648s4

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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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