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	1683b	Isogeny class
Conductor	1683	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	2912346798448923 = 39 · 116 · 174	Discriminant
Eigenvalues	-1 3+  4 -2 11+ -2 17-  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-12027773,16058584234]	[a1,a2,a3,a4,a6]
j	9776604686860471347243/147962546281	j-invariant
L	1.2858129035007	L(r)(E,1)/r!
Ω	0.32145322587518	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	26928bb2 107712t2 1683c2 42075a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1683b2

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	+	4	-2	+	-2	-	2	4	-6	4	10	6	-2	0	0	12	2	-8	-16	6	6	-4	16	2

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Quadratic twists for elliptic curve 1683b2

-4	8	-3	5	-7	-11	17
26928bb2	107712t2	1683c2	42075a2	82467b2	18513b2	28611f2

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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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