Cremona's table of elliptic curves

13320 = 2³ · 3² · 5 · 37

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 37-	Signs for the Atkin-Lehner involutions
Class	13320d	Isogeny class
Conductor	13320	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	186437376000 = 211 · 39 · 53 · 37	Discriminant
Eigenvalues	2+ 3- 5+  0  0  6 -2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-47952003,-127808060002]	[a1,a2,a3,a4,a6]
Generators	[37999257887342771463158:-51638019910611628773835388:20576905755257683]	Generators of the group modulo torsion
j	8167450100737631904002/124875	j-invariant
L	4.5292717008639	L(r)(E,1)/r!
Ω	0.057371719509965	Real period
R	39.473034271504	Regulator
r	1	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	26640g4 106560ck4 4440g4 66600bk4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13320d3

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
+	-	+	0	0	6	-2	-8	0	2	8	-	-10	4	-4	-6	4	2	-12	8	2	8	4	-10	-18

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Quadratic twists for elliptic curve 13320d3

-4	8	-3	5
26640g4	106560ck4	4440g4	66600bk4

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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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