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	15288t	Isogeny class
Conductor	15288	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-36663027518208 = -1 · 28 · 3 · 710 · 132	Discriminant
Eigenvalues	2+ 3- -4 7-  6 13- -6  8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-9620,462384]	[a1,a2,a3,a4,a6]
j	-3269383504/1217307	j-invariant
L	2.4476042970359	L(r)(E,1)/r!
Ω	0.61190107425898	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	30576r2 122304bo2 45864cd2 2184e2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 15288t2

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

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Quadratic twists for elliptic curve 15288t2

-4	8	-3	-7
30576r2	122304bo2	45864cd2	2184e2

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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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