Cremona's table of elliptic curves

1739 = 37 · 47

Field	Data	Notes
Atkin-Lehner	37+ 47+	Signs for the Atkin-Lehner involutions
Class	1739a	Isogeny class
Conductor	1739	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	2004	Modular degree for the optimal curve
Δ	-3841451 = -1 · 37 · 473	Discriminant
Eigenvalues	-2  3  1 -4 -2  1 -6 -3	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-1897,-31802]	[a1,a2,a3,a4,a6]
Generators	[1389:2206:27]	Generators of the group modulo torsion
j	-754963064303616/3841451	j-invariant
L	2.3639850481748	L(r)(E,1)/r!
Ω	0.36170340214011	Real period
R	6.5357003395259	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	27824b1 111296d1 15651c1 43475b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1739a1

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
-2	3	1	-4	-2	1	-6	-3	-4	-3	5	+	-6	-4	+	7	-4	-8	2	-9	-10	4	9	16	16

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Quadratic twists for elliptic curve 1739a1

-4	8	-3	5	-7	37	-47
27824b1	111296d1	15651c1	43475b1	85211i1	64343a1	81733a1

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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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