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	89280bq	Isogeny class
Conductor	89280	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	2211840	Modular degree for the optimal curve
Δ	-7.4030738665887E+19	Discriminant
Eigenvalues	2+ 3- 5+  2  0  4 -6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,800052,309032048]	[a1,a2,a3,a4,a6]
Generators	[-163764930:-16083095552:1157625]	Generators of the group modulo torsion
j	296354077829711/387386634240	j-invariant
L	6.3481474631077	L(r)(E,1)/r!
Ω	0.13054159379201	Real period
R	12.157327176786	Regulator
r	1	Rank of the group of rational points
S	0.99999999991705	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	89280eg1 2790l1 29760s1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 89280bq1

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

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Quadratic twists for elliptic curve 89280bq1

-4	8	-3
89280eg1	2790l1	29760s1

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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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