Cremona's table of elliptic curves

1083 = 3 · 19²

Field	Data	Notes
Atkin-Lehner	3- 19-	Signs for the Atkin-Lehner involutions
Class	1083d	Isogeny class
Conductor	1083	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	36	Modular degree for the optimal curve
Δ	-1083 = -1 · 3 · 192	Discriminant
Eigenvalues	-1 3-  0  1 -2 -5 -4 19-	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,2,-1]	[a1,a2,a3,a4,a6]
Generators	[1:1:1]	Generators of the group modulo torsion
j	2375/3	j-invariant
L	1.9597168743152	L(r)(E,1)/r!
Ω	2.624171538224	Real period
R	0.74679450095766	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	17328s1 69312k1 3249d1 27075d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1083d1

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
-1	-	0	1	-2	-5	-4	-	-4	8	3	-3	12	-1	-6	-4	-10	-13	-11	-6	-11	-1	0	6	-2

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Quadratic twists for elliptic curve 1083d1

-4	8	-3	5	-7	-19
17328s1	69312k1	3249d1	27075d1	53067i1	1083a1

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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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