Cremona's table of elliptic curves

14416 = 2⁴ · 17 · 53

Field	Data	Notes
Atkin-Lehner	2+ 17+ 53+	Signs for the Atkin-Lehner involutions
Class	14416a	Isogeny class
Conductor	14416	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	12224768 = 28 · 17 · 532	Discriminant
Eigenvalues	2+ -2  0  4  0  2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-108,364]	[a1,a2,a3,a4,a6]
Generators	[-2:24:1]	Generators of the group modulo torsion
j	549250000/47753	j-invariant
L	3.8528389228964	L(r)(E,1)/r!
Ω	2.1981484967771	Real period
R	1.7527655336049	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	7208a2 57664bd2 129744k2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 14416a2

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	0	2	+	-4	6	6	-10	-2	4	-4	0	+	4	-8	12	-6	-8	10	12	-10	-18

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Quadratic twists for elliptic curve 14416a2

-4	8	-3
7208a2	57664bd2	129744k2

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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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