Cremona's table of elliptic curves

15288 = 2³ · 3 · 7² · 13

Field	Data	Notes
Atkin-Lehner	2- 3+ 7- 13+	Signs for the Atkin-Lehner involutions
Class	15288u	Isogeny class
Conductor	15288	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-81256549911892992 = -1 · 210 · 32 · 714 · 13	Discriminant
Eigenvalues	2- 3+  2 7- -4 13+ -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,83088,10126908]	[a1,a2,a3,a4,a6]
Generators	[-82:1660:1]	Generators of the group modulo torsion
j	526556774012/674481717	j-invariant
L	4.4252850436114	L(r)(E,1)/r!
Ω	0.23001308450589	Real period
R	4.809818812175	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	30576v3 122304eg3 45864n3 2184m4	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 15288u4

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

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Quadratic twists for elliptic curve 15288u4

-4	8	-3	-7
30576v3	122304eg3	45864n3	2184m4

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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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