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	1752g	Isogeny class
Conductor	1752	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	4710927403008 = 211 · 34 · 734	Discriminant
Eigenvalues	2- 3+  2  0  0 -6 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-5232,-99828]	[a1,a2,a3,a4,a6]
Generators	[233:3358:1]	Generators of the group modulo torsion
j	7735350027746/2300257521	j-invariant
L	2.7418143785872	L(r)(E,1)/r!
Ω	0.57420863321398	Real period
R	2.3874722705236	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3504l3 14016bd3 5256g3 43800k4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1752g3

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	0	0	-6	-6	4	0	-6	0	-2	-6	-8	8	-6	8	14	12	0	-	-8	-16	10	-14

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Quadratic twists for elliptic curve 1752g3

-4	8	-3	5	-7	73
3504l3	14016bd3	5256g3	43800k4	85848v4	127896n4

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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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