Cremona's table of elliptic curves

1752 = 2³ · 3 · 73

Field	Data	Notes
Atkin-Lehner	2- 3- 73-	Signs for the Atkin-Lehner involutions
Class	1752k	Isogeny class
Conductor	1752	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	640	Modular degree for the optimal curve
Δ	122611968 = 28 · 38 · 73	Discriminant
Eigenvalues	2- 3-  2  4 -4  2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-132,-288]	[a1,a2,a3,a4,a6]
j	1001132368/478953	j-invariant
L	2.9517170879964	L(r)(E,1)/r!
Ω	1.4758585439982	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	3504f1 14016n1 5256h1 43800d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1752k1

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

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Quadratic twists for elliptic curve 1752k1

-4	8	-3	5	-7	73
3504f1	14016n1	5256h1	43800d1	85848n1	127896y1

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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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