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	4	Product of Tamagawa factors cp
Δ	-151330830336 = -1 · 211 · 34 · 7 · 194	Discriminant
Eigenvalues	2- 3+ -2 7-  0 -2  6 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-784,-20276]	[a1,a2,a3,a4,a6]
Generators	[1191:4600:27]	Generators of the group modulo torsion
j	-26055281954/73892007	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	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	6384i4 25536bp3 9576l4 79800i3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3192n4

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 3192n4

-4	8	-3	5	-7	-19
6384i4	25536bp3	9576l4	79800i3	22344bi3	60648s3

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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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