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	89280br	Isogeny class
Conductor	89280	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	208272384000000 = 216 · 38 · 56 · 31	Discriminant
Eigenvalues	2+ 3- 5+ -2  0  0 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-19308,-764368]	[a1,a2,a3,a4,a6]
Generators	[-98:432:1]	Generators of the group modulo torsion
j	16662038116/4359375	j-invariant
L	4.9325609052794	L(r)(E,1)/r!
Ω	0.41287407680199	Real period
R	1.4933611674791	Regulator
r	1	Rank of the group of rational points
S	0.99999999968382	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	89280ef2 11160s2 29760t2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 89280br2

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	0	-2	0	0	-8	-	8	-2	0	8	6	10	6	-14	6	-4	-16	-12	8	-10

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Quadratic twists for elliptic curve 89280br2

-4	8	-3
89280ef2	11160s2	29760t2

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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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