Cremona's table of elliptic curves

1683 = 3² · 11 · 17

Field	Data	Notes
Atkin-Lehner	3+ 11- 17-	Signs for the Atkin-Lehner involutions
Class	1683d	Isogeny class
Conductor	1683	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	-592783797771 = -1 · 39 · 116 · 17	Discriminant
Eigenvalues	-1 3+ -2 -2 11- -2 17-  8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,1699,24976]	[a1,a2,a3,a4,a6]
Generators	[17:233:1]	Generators of the group modulo torsion
j	27570978261/30116537	j-invariant
L	1.5837387746094	L(r)(E,1)/r!
Ω	0.60892078927826	Real period
R	0.86696485678461	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	26928y2 107712g2 1683a2 42075h2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1683d2

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	+	-2	-2	-	-2	-	8	4	6	-8	-2	6	-8	6	0	-6	-4	4	-4	0	-6	-16	4	2

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Quadratic twists for elliptic curve 1683d2

-4	8	-3	5	-7	-11	17
26928y2	107712g2	1683a2	42075h2	82467d2	18513a2	28611c2

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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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