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	13320g	Isogeny class
Conductor	13320	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	32367600000000 = 210 · 37 · 58 · 37	Discriminant
Eigenvalues	2+ 3- 5-  0 -4  6  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-23187,1331134]	[a1,a2,a3,a4,a6]
j	1846842725956/43359375	j-invariant
L	2.6248341970707	L(r)(E,1)/r!
Ω	0.65620854926767	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	26640o4 106560bb4 4440h3 66600bl4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13320g3

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

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Quadratic twists for elliptic curve 13320g3

-4	8	-3	5
26640o4	106560bb4	4440h3	66600bl4

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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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