Cremona's table of elliptic curves

82368 = 2⁶ · 3² · 11 · 13

Field	Data	Notes
Atkin-Lehner	2- 3- 11+ 13-	Signs for the Atkin-Lehner involutions
Class	82368dy	Isogeny class
Conductor	82368	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	688128	Modular degree for the optimal curve
Δ	-988476710756401152 = -1 · 214 · 320 · 113 · 13	Discriminant
Eigenvalues	2- 3-  0  0 11+ 13-  4  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,102660,-46128656]	[a1,a2,a3,a4,a6]
j	10017976862000/82759712607	j-invariant
L	2.2054489430965	L(r)(E,1)/r!
Ω	0.13784055982164	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	82368cc1 20592g1 27456ci1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 82368dy1

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	+	-	4	0	-8	0	10	2	6	-2	4	14	0	-6	6	8	-6	-2	12	8	-10

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Quadratic twists for elliptic curve 82368dy1

-4	8	-3
82368cc1	20592g1	27456ci1

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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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