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	14560o	Isogeny class
Conductor	14560	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	309120	Modular degree for the optimal curve
Δ	-3913929614067200 = -1 · 29 · 52 · 77 · 135	Discriminant
Eigenvalues	2- -3 5- 7+ -3 13+ -6 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-611467,-184062674]	[a1,a2,a3,a4,a6]
Generators	[3257:179930:1]	Generators of the group modulo torsion
j	-49382471573276665608/7644393777475	j-invariant
L	2.2947455702777	L(r)(E,1)/r!
Ω	0.085363511086739	Real period
R	6.7205107342234	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	14560s1 29120bp1 72800s1 101920bg1	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 14560o1

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	-	+	-3	+	-6	-6	-1	6	-9	7	1	2	13	12	4	5	7	8	-9	-5	-6	-14	-7

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Quadratic twists for elliptic curve 14560o1

-4	8	5	-7
14560s1	29120bp1	72800s1	101920bg1

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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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