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	1743c	Isogeny class
Conductor	1743	Conductor
∏ cp	30	Product of Tamagawa factors cp
deg	1920	Modular degree for the optimal curve
Δ	-333605122641 = -1 · 35 · 74 · 833	Discriminant
Eigenvalues	-1 3-  1 7+ -5 -2  0  7	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1315,33194]	[a1,a2,a3,a4,a6]
Generators	[335:5933:1]	Generators of the group modulo torsion
j	-251490515920561/333605122641	j-invariant
L	2.2474235501441	L(r)(E,1)/r!
Ω	0.86816731592825	Real period
R	0.086289954670819	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	27888w1 111552c1 5229a1 43575c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1743c1

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	-	1	+	-5	-2	0	7	3	4	-6	-9	-10	-4	0	-3	-3	7	1	-12	12	-4	-	7	-6

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Quadratic twists for elliptic curve 1743c1

-4	8	-3	5	-7
27888w1	111552c1	5229a1	43575c1	12201d1

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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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