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	81225x	Isogeny class
Conductor	81225	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	248832	Modular degree for the optimal curve
Δ	374707423828125 = 312 · 59 · 192	Discriminant
Eigenvalues	0 3- 5+ -2  3 -4  0 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-48450,-3997719]	[a1,a2,a3,a4,a6]
Generators	[-135:287:1]	Generators of the group modulo torsion
j	3058794496/91125	j-invariant
L	4.0337492398175	L(r)(E,1)/r!
Ω	0.32237953591138	Real period
R	3.1281058416945	Regulator
r	1	Rank of the group of rational points
S	1.0000000004237	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	27075p1 16245b1 81225o1	Quadratic twists by: -3 5 -19

Hecke Eigenvalues for elliptic curve 81225x1

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	-	+	-2	3	-4	0	-	-6	3	-5	8	-6	4	6	6	-9	-7	2	-9	4	7	0	3	-10

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Quadratic twists for elliptic curve 81225x1

-3	5	-19
27075p1	16245b1	81225o1

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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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