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	1752h	Isogeny class
Conductor	1752	Conductor
∏ cp	40	Product of Tamagawa factors cp
Δ	1103507712 = 28 · 310 · 73	Discriminant
Eigenvalues	2- 3-  0  0 -2 -6  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-308,-1440]	[a1,a2,a3,a4,a6]
Generators	[-14:18:1]	Generators of the group modulo torsion
j	12663250000/4310577	j-invariant
L	3.2828768703943	L(r)(E,1)/r!
Ω	1.170764619503	Real period
R	0.28040451647642	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	3504a2 14016a2 5256a2 43800e2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1752h2

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

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Quadratic twists for elliptic curve 1752h2

-4	8	-3	5	-7	73
3504a2	14016a2	5256a2	43800e2	85848q2	127896s2

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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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