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	15288j	Isogeny class
Conductor	15288	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-30967355188224 = -1 · 210 · 32 · 76 · 134	Discriminant
Eigenvalues	2+ 3-  2 7-  0 13+ -2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,6648,-165600]	[a1,a2,a3,a4,a6]
Generators	[123:1590:1]	Generators of the group modulo torsion
j	269676572/257049	j-invariant
L	6.6453563460787	L(r)(E,1)/r!
Ω	0.36027788156383	Real period
R	4.6112713867097	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	30576c3 122304cb3 45864bk3 312d4	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 15288j4

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	-	0	+	-2	-8	8	-2	-4	-10	-2	-4	12	6	0	2	8	-12	-10	-8	0	14	-2

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Quadratic twists for elliptic curve 15288j4

-4	8	-3	-7
30576c3	122304cb3	45864bk3	312d4

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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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