Cremona's table of elliptic curves

14288 = 2⁴ · 19 · 47

Field	Data	Notes
Atkin-Lehner	2- 19- 47-	Signs for the Atkin-Lehner involutions
Class	14288g	Isogeny class
Conductor	14288	Conductor
∏ cp	48	Product of Tamagawa factors cp
deg	228096	Modular degree for the optimal curve
Δ	-280764461436895232 = -1 · 223 · 193 · 474	Discriminant
Eigenvalues	2- -3  0 -3 -2 -1 -5 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-115435,29627674]	[a1,a2,a3,a4,a6]
Generators	[-422:1786:1] [53:4864:1]	Generators of the group modulo torsion
j	-41531372728322625/68546011092992	j-invariant
L	4.076090848184	L(r)(E,1)/r!
Ω	0.27655579629275	Real period
R	0.30705760094545	Regulator
r	2	Rank of the group of rational points
S	0.99999999999946	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1786e1 57152p1 128592h1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 14288g1

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
-	-3	0	-3	-2	-1	-5	-	5	-5	-4	-10	0	0	-	11	-3	-10	13	-14	-11	-14	-2	8	10

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Quadratic twists for elliptic curve 14288g1

-4	8	-3
1786e1	57152p1	128592h1

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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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