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	14288a	Isogeny class
Conductor	14288	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	13440	Modular degree for the optimal curve
Δ	-22004891648 = -1 · 219 · 19 · 472	Discriminant
Eigenvalues	2- -3  0 -1  0  3  3 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,605,4258]	[a1,a2,a3,a4,a6]
Generators	[7:94:1]	Generators of the group modulo torsion
j	5979018375/5372288	j-invariant
L	2.6709949998536	L(r)(E,1)/r!
Ω	0.78733371062621	Real period
R	0.8481140092837	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1786c1 57152t1 128592f1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 14288a1

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	-1	0	3	3	+	-7	-5	10	6	4	2	-	5	9	-10	-9	-4	3	-4	-16	18	8

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Quadratic twists for elliptic curve 14288a1

-4	8	-3
1786c1	57152t1	128592f1

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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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