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	8736j	Isogeny class
Conductor	8736	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	4769856 = 26 · 32 · 72 · 132	Discriminant
Eigenvalues	2+ 3-  2 7- -4 13+ -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-42,0]	[a1,a2,a3,a4,a6]
Generators	[56:420:1]	Generators of the group modulo torsion
j	131096512/74529	j-invariant
L	5.7811218296391	L(r)(E,1)/r!
Ω	2.0946677158777	Real period
R	2.7599231065709	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	8736n1 17472n2 26208bq1 61152m1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 8736j1

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

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Quadratic twists for elliptic curve 8736j1

-4	8	-3	-7	13
8736n1	17472n2	26208bq1	61152m1	113568co1

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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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