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	1683g	Isogeny class
Conductor	1683	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	2560	Modular degree for the optimal curve
Δ	-8049736827 = -1 · 316 · 11 · 17	Discriminant
Eigenvalues	0 3-  2 -3 11+  2 17-  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-33564,2366788]	[a1,a2,a3,a4,a6]
Generators	[106:4:1]	Generators of the group modulo torsion
j	-5736108018368512/11042163	j-invariant
L	2.5616126703055	L(r)(E,1)/r!
Ω	1.1265808964819	Real period
R	1.1368969056306	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	26928bx1 107712co1 561a1 42075u1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1683g1

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	-	2	-3	+	2	-	2	-2	-9	8	-12	3	0	-5	-11	-7	-2	3	4	-13	8	-16	-15	16

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Quadratic twists for elliptic curve 1683g1

-4	8	-3	5	-7	-11	17
26928bx1	107712co1	561a1	42075u1	82467o1	18513l1	28611q1

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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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