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	13520z	Isogeny class
Conductor	13520	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	42250000 = 24 · 56 · 132	Discriminant
Eigenvalues	2- -1 5- -1  3 13+ -3  5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-290,1975]	[a1,a2,a3,a4,a6]
Generators	[5:25:1]	Generators of the group modulo torsion
j	1000939264/15625	j-invariant
L	3.9499583222349	L(r)(E,1)/r!
Ω	2.0370340483244	Real period
R	0.32317888234646	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	3380e2 54080ca2 121680dg2 67600bl2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13520z2

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	-	-1	3	+	-3	5	-9	-9	8	7	-3	1	0	6	9	-1	5	9	-2	-8	0	-3	-17

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Quadratic twists for elliptic curve 13520z2

-4	8	-3	5	13
3380e2	54080ca2	121680dg2	67600bl2	13520q2

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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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