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	4	Product of Tamagawa factors cp
Δ	47943168 = 29 · 3 · 74 · 13	Discriminant
Eigenvalues	2+ 3-  2 7- -4 13+ -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-432,-3588]	[a1,a2,a3,a4,a6]
Generators	[7195:50862:125]	Generators of the group modulo torsion
j	17454600584/93639	j-invariant
L	5.7811218296391	L(r)(E,1)/r!
Ω	1.0473338579389	Real period
R	5.5198462131418	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	8736n3 17472n3 26208bq3 61152m3	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 8736j2

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 8736j2

-4	8	-3	-7	13
8736n3	17472n3	26208bq3	61152m3	113568co3

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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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