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	13520bf	Isogeny class
Conductor	13520	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	29952	Modular degree for the optimal curve
Δ	326292288400 = 24 · 52 · 138	Discriminant
Eigenvalues	2-  3 5- -3 -3 13+ -7 -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-2197,-28561]	[a1,a2,a3,a4,a6]
Generators	[-1014:845:27]	Generators of the group modulo torsion
j	89856/25	j-invariant
L	7.7078494392014	L(r)(E,1)/r!
Ω	0.71198604512466	Real period
R	1.8043072360713	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	3380j1 54080co1 121680dx1 67600cm1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13520bf1

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	-3	+	-7	-1	7	-5	4	-3	7	9	-8	-6	-5	-5	-13	3	-14	8	-12	7	-11

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Quadratic twists for elliptic curve 13520bf1

-4	8	-3	5	13
3380j1	54080co1	121680dx1	67600cm1	13520u1

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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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