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
deg	768	Modular degree for the optimal curve
Δ	1513728 = 28 · 34 · 73	Discriminant
Eigenvalues	2- 3+  2  0  0 -6 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1972,34372]	[a1,a2,a3,a4,a6]
Generators	[1:180:1]	Generators of the group modulo torsion
j	3314550883408/5913	j-invariant
L	2.7418143785872	L(r)(E,1)/r!
Ω	2.2968345328559	Real period
R	2.3874722705236	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	3504l1 14016bd1 5256g1 43800k1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1752g1

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 1752g1

-4	8	-3	5	-7	73
3504l1	14016bd1	5256g1	43800k1	85848v1	127896n1

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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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