Cremona's table of elliptic curves

129200 = 2⁴ · 5² · 17 · 19

Field	Data	Notes
Atkin-Lehner	2- 5- 17+ 19+	Signs for the Atkin-Lehner involutions
Class	129200cp	Isogeny class
Conductor	129200	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1472256	Modular degree for the optimal curve
Δ	-5617347442936832000 = -1 · 213 · 53 · 17 · 199	Discriminant
Eigenvalues	2-  1 5-  0 -3  6 17+ 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-374688,144083828]	[a1,a2,a3,a4,a6]
Generators	[-542:13720:1]	Generators of the group modulo torsion
j	-11362247972535797/10971381724486	j-invariant
L	8.0617619999102	L(r)(E,1)/r!
Ω	0.21925848612248	Real period
R	4.5960375861067	Regulator
r	1	Rank of the group of rational points
S	1.0000000066457	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	16150z1 129200db1	Quadratic twists by: -4 5

Hecke Eigenvalues for elliptic curve 129200cp1

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
-	1	-	0	-3	6	+	+	1	4	-5	1	9	5	-6	0	4	6	-2	-3	-7	1	-5	-10	0

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Quadratic twists for elliptic curve 129200cp1

-4	5
16150z1	129200db1

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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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