Cremona's table of elliptic curves

81225 = 3² · 5² · 19²

Field	Data	Notes
Atkin-Lehner	3- 5+ 19-	Signs for the Atkin-Lehner involutions
Class	81225w	Isogeny class
Conductor	81225	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-10181757777046875 = -1 · 36 · 56 · 197	Discriminant
Eigenvalues	0 3- 5+  1 -3 -4 -3 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-62489100,-190131694344]	[a1,a2,a3,a4,a6]
Generators	[22202769870505978358586854:-1150835684727557029534808936:2129199263584182248311]	Generators of the group modulo torsion
j	-50357871050752/19	j-invariant
L	4.1144883804056	L(r)(E,1)/r!
Ω	0.026848405071793	Real period
R	38.312223476622	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	9025c3 3249c3 4275k3	Quadratic twists by: -3 5 -19

Hecke Eigenvalues for elliptic curve 81225w3

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
0	-	+	1	-3	-4	-3	-	0	6	4	2	-6	1	-3	-12	-6	-1	-4	6	7	-8	12	12	8

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Quadratic twists for elliptic curve 81225w3

-3	5	-19
9025c3	3249c3	4275k3

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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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