Cremona's table of elliptic curves

1743 = 3 · 7 · 83

Field	Data	Notes
Atkin-Lehner	3+ 7- 83+	Signs for the Atkin-Lehner involutions
Class	1743a	Isogeny class
Conductor	1743	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	21266343 = 32 · 73 · 832	Discriminant
Eigenvalues	1 3+  2 7-  6 -4  4 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-1834,-31007]	[a1,a2,a3,a4,a6]
j	682797081921193/21266343	j-invariant
L	2.188471821096	L(r)(E,1)/r!
Ω	0.72949060703199	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	27888bh2 111552bx2 5229c2 43575p2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1743a2

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

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Quadratic twists for elliptic curve 1743a2

-4	8	-3	5	-7
27888bh2	111552bx2	5229c2	43575p2	12201l2

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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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