Cremona's table of elliptic curves

1992 = 2³ · 3 · 83

Field	Data	Notes
Atkin-Lehner	2- 3- 83-	Signs for the Atkin-Lehner involutions
Class	1992a	Isogeny class
Conductor	1992	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	-10285221888 = -1 · 211 · 36 · 832	Discriminant
Eigenvalues	2- 3- -2 -4  0 -4  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-704,-8928]	[a1,a2,a3,a4,a6]
j	-18868113794/5022081	j-invariant
L	1.371040417813	L(r)(E,1)/r!
Ω	0.45701347260433	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3984a2 15936b2 5976d2 49800e2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1992a2

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

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Quadratic twists for elliptic curve 1992a2

-4	8	-3	5	-7
3984a2	15936b2	5976d2	49800e2	97608o2

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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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