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	3192h	Isogeny class
Conductor	3192	Conductor
∏ cp	40	Product of Tamagawa factors cp
deg	640	Modular degree for the optimal curve
Δ	-68774832 = -1 · 24 · 35 · 72 · 192	Discriminant
Eigenvalues	2+ 3-  0 7-  0 -2 -8 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,37,402]	[a1,a2,a3,a4,a6]
Generators	[1:21:1]	Generators of the group modulo torsion
j	340736000/4298427	j-invariant
L	4.0440389970535	L(r)(E,1)/r!
Ω	1.4429373117644	Real period
R	0.28026435826989	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	6384b1 25536r1 9576y1 79800v1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3192h1

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
+	-	0	-	0	-2	-8	+	-4	0	0	-2	2	-4	-6	-12	-4	-2	4	6	6	4	-6	18	14

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Quadratic twists for elliptic curve 3192h1

-4	8	-3	5	-7	-19
6384b1	25536r1	9576y1	79800v1	22344f1	60648z1

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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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