Cremona's table of elliptic curves

82800 = 2⁴ · 3² · 5² · 23

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 23+	Signs for the Atkin-Lehner involutions
Class	82800do	Isogeny class
Conductor	82800	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	414720	Modular degree for the optimal curve
Δ	-1385897343750000 = -1 · 24 · 36 · 510 · 233	Discriminant
Eigenvalues	2- 3- 5+ -4 -6  1  0 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-10425,1837375]	[a1,a2,a3,a4,a6]
Generators	[270:4325:1]	Generators of the group modulo torsion
j	-687518464/7604375	j-invariant
L	3.4628418920571	L(r)(E,1)/r!
Ω	0.40898254300514	Real period
R	4.2334837426485	Regulator
r	1	Rank of the group of rational points
S	0.99999999953173	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	20700r1 9200bb1 16560cg1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 82800do1

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	-6	1	0	-2	+	-9	-5	-2	9	-4	3	-6	0	2	-10	-3	7	10	12	0	-8

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Quadratic twists for elliptic curve 82800do1

-4	-3	5
20700r1	9200bb1	16560cg1

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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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