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	13520bb	Isogeny class
Conductor	13520	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-30891577600 = -1 · 28 · 52 · 136	Discriminant
Eigenvalues	2-  2 5-  2  0 13+ -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,620,-6228]	[a1,a2,a3,a4,a6]
Generators	[29493:210574:729]	Generators of the group modulo torsion
j	21296/25	j-invariant
L	7.3819699201132	L(r)(E,1)/r!
Ω	0.63073994107834	Real period
R	5.8518332511912	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	3380i2 54080ck2 121680dm2 67600cc2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13520bb2

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

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Quadratic twists for elliptic curve 13520bb2

-4	8	-3	5	13
3380i2	54080ck2	121680dm2	67600cc2	80b1

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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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