Cremona's table of elliptic curves

27225 = 3² · 5² · 11²

Field	Data	Notes
Atkin-Lehner	3- 5+ 11+	Signs for the Atkin-Lehner involutions
Class	27225ba	Isogeny class
Conductor	27225	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	12960	Modular degree for the optimal curve
Δ	-15160921875 = -1 · 36 · 56 · 113	Discriminant
Eigenvalues	0 3- 5+  0 11+  0  0  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-1650,-26469]	[a1,a2,a3,a4,a6]
j	-32768	j-invariant
L	0.74773598571861	L(r)(E,1)/r!
Ω	0.37386799285958	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	3025a1 1089e1 27225ba2	Quadratic twists by: -3 5 -11

Hecke Eigenvalues for elliptic curve 27225ba1

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	-	+	0	+	0	0	0	-9	0	-5	-7	0	0	-12	6	15	0	-13	3	0	0	0	9	-17

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Quadratic twists for elliptic curve 27225ba1

-3	5	-11
3025a1	1089e1	27225ba2

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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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