Cremona's table of elliptic curves

13872 = 2⁴ · 3 · 17²

Field	Data	Notes
Atkin-Lehner	2- 3- 17+	Signs for the Atkin-Lehner involutions
Class	13872bi	Isogeny class
Conductor	13872	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	-2.8940262395316E+20	Discriminant
Eigenvalues	2- 3-  2  0 -4 -2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,1044928,708081972]	[a1,a2,a3,a4,a6]
Generators	[-9564:1499043:64]	Generators of the group modulo torsion
j	1276229915423/2927177028	j-invariant
L	6.2576347859517	L(r)(E,1)/r!
Ω	0.12047737175751	Real period
R	6.4925416020725	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	1734i4 55488cp3 41616ci3 816h4	Quadratic twists by: -4 8 -3 17

Hecke Eigenvalues for elliptic curve 13872bi4

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

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Quadratic twists for elliptic curve 13872bi4

-4	8	-3	17
1734i4	55488cp3	41616ci3	816h4

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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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