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	13520s	Isogeny class
Conductor	13520	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	44928	Modular degree for the optimal curve
Δ	-133649321328640 = -1 · 215 · 5 · 138	Discriminant
Eigenvalues	2-  2 5+  1 -3 13+ -6 -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-27096,-1795600]	[a1,a2,a3,a4,a6]
j	-658489/40	j-invariant
L	2.2248353053349	L(r)(E,1)/r!
Ω	0.18540294211124	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	1690c1 54080df1 121680es1 67600cb1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13520s1

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	+	1	-3	+	-6	-5	0	0	4	11	6	-2	3	-9	0	8	16	-6	14	16	6	9	-10

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Quadratic twists for elliptic curve 13520s1

-4	8	-3	5	13
1690c1	54080df1	121680es1	67600cb1	13520ba1

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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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