Cremona's table of elliptic curves

53280 = 2⁵ · 3² · 5 · 37

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 37-	Signs for the Atkin-Lehner involutions
Class	53280o	Isogeny class
Conductor	53280	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	419716106956800 = 212 · 37 · 52 · 374	Discriminant
Eigenvalues	2+ 3- 5+ -4 -4 -2  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-20028,467552]	[a1,a2,a3,a4,a6]
Generators	[181:1665:1]	Generators of the group modulo torsion
j	297542483776/140562075	j-invariant
L	3.0681866782723	L(r)(E,1)/r!
Ω	0.47381091721708	Real period
R	0.80944385375571	Regulator
r	1	Rank of the group of rational points
S	1.0000000000008	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	53280bq3 106560cy1 17760v3	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 53280o3

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
+	-	+	-4	-4	-2	2	0	-8	-6	0	-	-2	-8	8	6	-4	14	4	8	-6	0	-4	-14	2

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Quadratic twists for elliptic curve 53280o3

-4	8	-3
53280bq3	106560cy1	17760v3

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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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