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	82800bg	Isogeny class
Conductor	82800	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	-97921962720000000 = -1 · 211 · 37 · 57 · 234	Discriminant
Eigenvalues	2+ 3- 5+  0  4 -2  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,104325,-7645750]	[a1,a2,a3,a4,a6]
Generators	[1295:47950:1]	Generators of the group modulo torsion
j	5382838942/4197615	j-invariant
L	7.4872571390152	L(r)(E,1)/r!
Ω	0.18767702410498	Real period
R	4.986796580389	Regulator
r	1	Rank of the group of rational points
S	1.0000000003768	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	41400bm3 27600b3 16560r4	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 82800bg3

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

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Quadratic twists for elliptic curve 82800bg3

-4	-3	5
41400bm3	27600b3	16560r4

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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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