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
deg	28800	Modular degree for the optimal curve
Δ	182751402669611193 = 39 · 113 · 178	Discriminant
Eigenvalues	-1 3+  4 -2 11+ -2 17-  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-752438,250564564]	[a1,a2,a3,a4,a6]
j	2393558463315519963/9284733153971	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	26928bb1 107712t1 1683c1 42075a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1683b1

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 1683b1

-4	8	-3	5	-7	-11	17
26928bb1	107712t1	1683c1	42075a1	82467b1	18513b1	28611f1

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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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