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	89280dj	Isogeny class
Conductor	89280	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	1249634304000000 = 217 · 39 · 56 · 31	Discriminant
Eigenvalues	2- 3+ 5+  4 -2  2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-138348,19733328]	[a1,a2,a3,a4,a6]
Generators	[11856:178388:27]	Generators of the group modulo torsion
j	113511836214/484375	j-invariant
L	7.2705135654949	L(r)(E,1)/r!
Ω	0.48714105797316	Real period
R	7.4624315138526	Regulator
r	1	Rank of the group of rational points
S	1.0000000000102	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	89280h2 22320d2 89280dv2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 89280dj2

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	-2	2	-2	4	-8	4	-	-2	0	4	-12	6	-8	-14	2	10	0	4	0	6	-10

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Quadratic twists for elliptic curve 89280dj2

-4	8	-3
89280h2	22320d2	89280dv2

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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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