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	13520c	Isogeny class
Conductor	13520	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	11424400 = 24 · 52 · 134	Discriminant
Eigenvalues	2+  1 5+  3  3 13+ -3  5	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-56,-25]	[a1,a2,a3,a4,a6]
Generators	[17:65:1]	Generators of the group modulo torsion
j	43264/25	j-invariant
L	5.8614684361464	L(r)(E,1)/r!
Ω	1.90465178635	Real period
R	0.51290814049351	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	6760h1 54080da1 121680bo1 67600k1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13520c1

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	+	3	3	+	-3	5	-3	-5	0	-11	-5	7	8	-10	1	-5	-11	-3	-6	0	16	-13	-7

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Quadratic twists for elliptic curve 13520c1

-4	8	-3	5	13
6760h1	54080da1	121680bo1	67600k1	13520k1

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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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