Cremona's table of elliptic curves

13520 = 2⁴ · 5 · 13²

Field	Data	Notes
Atkin-Lehner	2- 5+ 13+	Signs for the Atkin-Lehner involutions
Class	13520q	Isogeny class
Conductor	13520	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	14976	Modular degree for the optimal curve
Δ	326292288400 = 24 · 52 · 138	Discriminant
Eigenvalues	2- -1 5+  1 -3 13+ -3 -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-5126,-136865]	[a1,a2,a3,a4,a6]
Generators	[-39:47:1] [113:845:1]	Generators of the group modulo torsion
j	1141504/25	j-invariant
L	5.4326063734416	L(r)(E,1)/r!
Ω	0.5649715931615	Real period
R	1.6026193290659	Regulator
r	2	Rank of the group of rational points
S	0.99999999999979	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	3380b1 54080cx1 121680er1 67600bo1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13520q1

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
-	-1	+	1	-3	+	-3	-5	-9	-9	-8	-7	3	1	0	6	-9	-1	-5	-9	2	-8	0	3	17

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Quadratic twists for elliptic curve 13520q1

-4	8	-3	5	13
3380b1	54080cx1	121680er1	67600bo1	13520z1

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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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