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	81225l	Isogeny class
Conductor	81225	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	184320	Modular degree for the optimal curve
Δ	-57319525263375 = -1 · 33 · 53 · 198	Discriminant
Eigenvalues	1 3+ 5- -2 -2 -2 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-34182,-2451049]	[a1,a2,a3,a4,a6]
Generators	[136570:4374903:125]	Generators of the group modulo torsion
j	-27818127/361	j-invariant
L	5.1671645833833	L(r)(E,1)/r!
Ω	0.17542205152805	Real period
R	7.3639039923924	Regulator
r	1	Rank of the group of rational points
S	1.0000000001895	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	81225n1 81225m1 4275d1	Quadratic twists by: -3 5 -19

Hecke Eigenvalues for elliptic curve 81225l1

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
1	+	-	-2	-2	-2	-2	-	0	-6	4	2	2	10	0	-10	0	-10	-4	-8	-4	8	12	10	-18

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Quadratic twists for elliptic curve 81225l1

-3	5	-19
81225n1	81225m1	4275d1

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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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