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	1752d	Isogeny class
Conductor	1752	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-338911183763500032 = -1 · 210 · 37 · 736	Discriminant
Eigenvalues	2- 3+  4  0 -2 -2  8 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-83016,-29455812]	[a1,a2,a3,a4,a6]
j	-61789459762658596/330967952894043	j-invariant
L	2.0244278622809	L(r)(E,1)/r!
Ω	0.12652674139256	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	16	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3504h2 14016w2 5256e2 43800p2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1752d2

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
-	+	4	0	-2	-2	8	-4	4	0	8	-6	6	4	-6	4	10	-2	-4	-4	+	16	-10	-6	2

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Quadratic twists for elliptic curve 1752d2

-4	8	-3	5	-7	73
3504h2	14016w2	5256e2	43800p2	85848ba2	127896q2

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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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