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	89280ei	Isogeny class
Conductor	89280	Conductor
∏ cp	1	Product of Tamagawa factors cp
Δ	-44477724672000 = -1 · 214 · 36 · 53 · 313	Discriminant
Eigenvalues	2- 3- 5+  4  0 -2  3 -7	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,2112,318688]	[a1,a2,a3,a4,a6]
Generators	[107230881:1350229135:912673]	Generators of the group modulo torsion
j	87228416/3723875	j-invariant
L	6.942174415237	L(r)(E,1)/r!
Ω	0.48494597436277	Real period
R	14.315356298834	Regulator
r	1	Rank of the group of rational points
S	1.0000000009433	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	89280bu2 22320bx2 9920z2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 89280ei2

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	0	-2	3	-7	0	-6	+	-5	3	-1	6	9	3	4	-10	3	-1	10	9	-12	2

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Quadratic twists for elliptic curve 89280ei2

-4	8	-3
89280bu2	22320bx2	9920z2

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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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