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	8736y	Isogeny class
Conductor	8736	Conductor
∏ cp	48	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	-2418316992 = -1 · 26 · 33 · 72 · 134	Discriminant
Eigenvalues	2- 3-  0 7- -6 13-  8  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-358,3404]	[a1,a2,a3,a4,a6]
Generators	[-10:78:1]	Generators of the group modulo torsion
j	-79507000000/37786203	j-invariant
L	5.2449024719219	L(r)(E,1)/r!
Ω	1.3541410390155	Real period
R	0.32276933746225	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	8736c1 17472g2 26208u1 61152bd1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 8736y1

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
-	-	0	-	-6	-	8	4	-6	6	-8	-6	-8	-8	-8	2	-12	-6	4	2	14	4	-8	8	-18

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Quadratic twists for elliptic curve 8736y1

-4	8	-3	-7	13
8736c1	17472g2	26208u1	61152bd1	113568y1

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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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