Cremona's table of elliptic curves

8736 = 2⁵ · 3 · 7 · 13

Field	Data	Notes
Atkin-Lehner	2- 3+ 7- 13+	Signs for the Atkin-Lehner involutions
Class	8736s	Isogeny class
Conductor	8736	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	16828051968 = 29 · 34 · 74 · 132	Discriminant
Eigenvalues	2- 3+  2 7-  0 13+ -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-146032,21528052]	[a1,a2,a3,a4,a6]
Generators	[-227:6552:1]	Generators of the group modulo torsion
j	672668087746709384/32867289	j-invariant
L	4.3084566346815	L(r)(E,1)/r!
Ω	0.92283798511636	Real period
R	2.3343515894278	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	8736v2 17472dd3 26208q4 61152cc4	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 8736s3

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

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Quadratic twists for elliptic curve 8736s3

-4	8	-3	-7	13
8736v2	17472dd3	26208q4	61152cc4	113568c4

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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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