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	82368w	Isogeny class
Conductor	82368	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	316537045254144 = 218 · 310 · 112 · 132	Discriminant
Eigenvalues	2+ 3- -2  0 11+ 13+  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-247116,-47274640]	[a1,a2,a3,a4,a6]
j	8732907467857/1656369	j-invariant
L	0.85652349554603	L(r)(E,1)/r!
Ω	0.21413086986503	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	82368eq2 1287e2 27456p2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 82368w2

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

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Quadratic twists for elliptic curve 82368w2

-4	8	-3
82368eq2	1287e2	27456p2

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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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