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	53280k	Isogeny class
Conductor	53280	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	69120	Modular degree for the optimal curve
Δ	1726272000000 = 212 · 36 · 56 · 37	Discriminant
Eigenvalues	2+ 3- 5+ -1 -1 -2  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-6168,175408]	[a1,a2,a3,a4,a6]
Generators	[36:4:1] [84:-500:1]	Generators of the group modulo torsion
j	8690991616/578125	j-invariant
L	9.1716708031724	L(r)(E,1)/r!
Ω	0.82364085781237	Real period
R	2.783880472957	Regulator
r	2	Rank of the group of rational points
S	0.99999999999986	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	53280j1 106560gc1 5920l1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 53280k1

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	-2	2	0	-4	-6	-10	+	-11	-8	-7	5	-10	-12	-8	1	-11	4	7	10	-8

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Quadratic twists for elliptic curve 53280k1

-4	8	-3
53280j1	106560gc1	5920l1

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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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