Cremona's table of elliptic curves

83205 = 3² · 5 · 43²

Field	Data	Notes
Atkin-Lehner	3- 5- 43+	Signs for the Atkin-Lehner involutions
Class	83205p	Isogeny class
Conductor	83205	Conductor
∏ cp	80	Product of Tamagawa factors cp
Δ	137543227822265625 = 311 · 510 · 433	Discriminant
Eigenvalues	-1 3- 5- -4 -4  2 -8  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-476357,-125162044]	[a1,a2,a3,a4,a6]
Generators	[-384:1204:1]	Generators of the group modulo torsion
j	206246988924787/2373046875	j-invariant
L	2.1004015599662	L(r)(E,1)/r!
Ω	0.18185217993939	Real period
R	0.57750244276953	Regulator
r	1	Rank of the group of rational points
S	0.99999999867022	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	27735f2 83205i2	Quadratic twists by: -3 -43

Hecke Eigenvalues for elliptic curve 83205p2

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	-	-	-4	-4	2	-8	2	-6	6	-8	-2	-10	+	10	-4	0	8	4	-12	10	-16	-6	2	6

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Quadratic twists for elliptic curve 83205p2

-3	-43
27735f2	83205i2

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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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