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	8736g	Isogeny class
Conductor	8736	Conductor
∏ cp	36	Product of Tamagawa factors cp
deg	6912	Modular degree for the optimal curve
Δ	-45921447936 = -1 · 212 · 36 · 7 · 133	Discriminant
Eigenvalues	2+ 3- -3 7+ -4 13-  4  3	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-397,10619]	[a1,a2,a3,a4,a6]
Generators	[29:-156:1]	Generators of the group modulo torsion
j	-1693669888/11211291	j-invariant
L	3.9907587331669	L(r)(E,1)/r!
Ω	0.97754592093061	Real period
R	0.11340071794183	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	8736e1 17472bs1 26208bn1 61152f1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 8736g1

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
+	-	-3	+	-4	-	4	3	5	-7	-1	-2	2	7	-5	1	4	-8	-8	-6	9	11	-13	3	1

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Quadratic twists for elliptic curve 8736g1

-4	8	-3	-7	13
8736e1	17472bs1	26208bn1	61152f1	113568cw1

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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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