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	13520u	Isogeny class
Conductor	13520	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	67600 = 24 · 52 · 132	Discriminant
Eigenvalues	2-  3 5+  3  3 13+ -7  1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-13,-13]	[a1,a2,a3,a4,a6]
j	89856/25	j-invariant
L	5.1342043862235	L(r)(E,1)/r!
Ω	2.5671021931118	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	3380d1 54080dh1 121680fd1 67600cn1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13520u1

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 13520u1

-4	8	-3	5	13
3380d1	54080dh1	121680fd1	67600cn1	13520bf1

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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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