Cremona's table of elliptic curves

14560 = 2⁵ · 5 · 7 · 13

Field	Data	Notes
Atkin-Lehner	2- 5+ 7+ 13-	Signs for the Atkin-Lehner involutions
Class	14560k	Isogeny class
Conductor	14560	Conductor
∏ cp	20	Product of Tamagawa factors cp
deg	217600	Modular degree for the optimal curve
Δ	33561946440626240 = 26 · 5 · 710 · 135	Discriminant
Eigenvalues	2-  2 5+ 7+  4 13- -8  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-630026,-192068320]	[a1,a2,a3,a4,a6]
Generators	[-341541:158158:729]	Generators of the group modulo torsion
j	432135399877565634496/524405413134785	j-invariant
L	6.4002683641742	L(r)(E,1)/r!
Ω	0.16946949097554	Real period
R	7.5532986230519	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	14560d1 29120p1 72800n1 101920bp1	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 14560k1

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	+	+	4	-	-8	2	6	-2	-4	2	0	-8	-8	12	-10	2	-4	2	10	-12	0	-16	-10

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Quadratic twists for elliptic curve 14560k1

-4	8	5	-7
14560d1	29120p1	72800n1	101920bp1

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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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