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	1752i	Isogeny class
Conductor	1752	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	-255792 = -1 · 24 · 3 · 732	Discriminant
Eigenvalues	2- 3-  0 -4  2  2 -8 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-23,42]	[a1,a2,a3,a4,a6]
Generators	[3:3:1]	Generators of the group modulo torsion
j	-87808000/15987	j-invariant
L	3.1547064950979	L(r)(E,1)/r!
Ω	2.989650843408	Real period
R	1.0552090061132	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	3504c1 14016c1 5256b1 43800i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1752i1

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
-	-	0	-4	2	2	-8	-4	4	-4	4	-6	-2	-4	2	-8	6	-2	-12	-4	+	0	-6	-14	2

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Quadratic twists for elliptic curve 1752i1

-4	8	-3	5	-7	73
3504c1	14016c1	5256b1	43800i1	85848p1	127896t1

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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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