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	8736w	Isogeny class
Conductor	8736	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1280	Modular degree for the optimal curve
Δ	-3354624 = -1 · 212 · 32 · 7 · 13	Discriminant
Eigenvalues	2- 3-  3 7-  0 13+  0  5	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-29,-117]	[a1,a2,a3,a4,a6]
j	-681472/819	j-invariant
L	3.9226599313171	L(r)(E,1)/r!
Ω	0.98066498282928	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	8736a1 17472r1 26208s1 61152bn1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 8736w1

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	-	0	+	0	5	-3	1	5	2	-2	-9	13	1	12	-4	0	-10	-1	-1	9	9	7

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Quadratic twists for elliptic curve 8736w1

-4	8	-3	-7	13
8736a1	17472r1	26208s1	61152bn1	113568bf1

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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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