Cremona's table of elliptic curves

89280 = 2⁶ · 3² · 5 · 31

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 31-	Signs for the Atkin-Lehner involutions
Class	89280fx	Isogeny class
Conductor	89280	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	-43042959360 = -1 · 212 · 37 · 5 · 312	Discriminant
Eigenvalues	2- 3- 5- -2  4  4 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,348,9664]	[a1,a2,a3,a4,a6]
Generators	[-10:72:1]	Generators of the group modulo torsion
j	1560896/14415	j-invariant
L	7.2982215795154	L(r)(E,1)/r!
Ω	0.8368143087242	Real period
R	1.090179372168	Regulator
r	1	Rank of the group of rational points
S	0.9999999997076	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	89280fg2 44640bn1 29760co2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 89280fx2

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
-	-	-	-2	4	4	-6	-4	0	0	-	4	6	8	8	-10	10	10	2	-10	-8	-8	4	-16	-2

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Quadratic twists for elliptic curve 89280fx2

-4	8	-3
89280fg2	44640bn1	29760co2

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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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