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	8736m	Isogeny class
Conductor	8736	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	11520	Modular degree for the optimal curve
Δ	-27779641344 = -1 · 212 · 32 · 73 · 133	Discriminant
Eigenvalues	2- 3+ -1 7+ -4 13+  0  7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-15421,-732011]	[a1,a2,a3,a4,a6]
j	-99021508447744/6782139	j-invariant
L	0.85683517025587	L(r)(E,1)/r!
Ω	0.21420879256397	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	8736i1 17472ba1 26208i1 61152cb1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 8736m1

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	+	0	7	3	5	-1	-2	-10	5	-5	-11	4	0	-4	-2	-9	5	-9	-11	7

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Quadratic twists for elliptic curve 8736m1

-4	8	-3	-7	13
8736i1	17472ba1	26208i1	61152cb1	113568p1

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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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