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	82800ds	Isogeny class
Conductor	82800	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	2.3096459872224E+27	Discriminant
Eigenvalues	2- 3- 5+  0  0 -6  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-364071675,-1342679521750]	[a1,a2,a3,a4,a6]
j	114387056741228939569/49503729150000000	j-invariant
L	0.28759719520612	L(r)(E,1)/r!
Ω	0.035949646836469	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	10350bh3 27600bg3 16560br4	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 82800ds3

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	-6	2	0	-	-6	-8	-10	6	-8	-8	-6	-4	-6	8	-8	-10	8	8	6	-18

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Quadratic twists for elliptic curve 82800ds3

-4	-3	5
10350bh3	27600bg3	16560br4

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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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