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	13320c	Isogeny class
Conductor	13320	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	299520	Modular degree for the optimal curve
Δ	-3014247940503091200 = -1 · 211 · 319 · 52 · 373	Discriminant
Eigenvalues	2+ 3- 5+  3  1  3 -3 -7	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1106643,455803342]	[a1,a2,a3,a4,a6]
j	-100389630395083682/2018931072975	j-invariant
L	2.027120046851	L(r)(E,1)/r!
Ω	0.25339000585638	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	26640f1 106560df1 4440i1 66600bs1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13320c1

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
+	-	+	3	1	3	-3	-7	-3	-10	10	+	12	-12	4	-9	6	2	10	-2	15	4	-9	11	8

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Quadratic twists for elliptic curve 13320c1

-4	8	-3	5
26640f1	106560df1	4440i1	66600bs1

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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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