Cremona's table of elliptic curves

88752 = 2⁴ · 3 · 43²

Field	Data	Notes
Atkin-Lehner	2- 3- 43+	Signs for the Atkin-Lehner involutions
Class	88752bc	Isogeny class
Conductor	88752	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1387008	Modular degree for the optimal curve
Δ	-861747630066966528 = -1 · 213 · 32 · 438	Discriminant
Eigenvalues	2- 3- -2  4 -3  2  3 -1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-503544,144434772]	[a1,a2,a3,a4,a6]
Generators	[414:2664:1]	Generators of the group modulo torsion
j	-294937/18	j-invariant
L	8.7816868153583	L(r)(E,1)/r!
Ω	0.27706928683027	Real period
R	3.9618640629714	Regulator
r	1	Rank of the group of rational points
S	1.0000000013426	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	11094c1 88752w1	Quadratic twists by: -4 -43

Hecke Eigenvalues for elliptic curve 88752bc1

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	4	-3	2	3	-1	6	-2	2	4	-5	+	6	14	5	-12	-7	-6	7	10	-16	1	-11

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Quadratic twists for elliptic curve 88752bc1

-4	-43
11094c1	88752w1

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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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