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	27225d	Isogeny class
Conductor	27225	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	16128	Modular degree for the optimal curve
Δ	-6176671875 = -1 · 33 · 56 · 114	Discriminant
Eigenvalues	0 3+ 5+ -5 11- -2  0 -7	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,0,3781]	[a1,a2,a3,a4,a6]
Generators	[-110:271:8] [-11:49:1]	Generators of the group modulo torsion
j	0	j-invariant
L	6.0429822236409	L(r)(E,1)/r!
Ω	1.0657445237234	Real period
R	0.47251648097673	Regulator
r	2	Rank of the group of rational points
S	1.0000000000001	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	27225d2 1089a1 27225a1	Quadratic twists by: -3 5 -11

Hecke Eigenvalues for elliptic curve 27225d1

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	+	+	-5	-	-2	0	-7	0	0	11	-11	0	-8	0	0	0	-1	-11	0	-17	-13	0	0	-5

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Quadratic twists for elliptic curve 27225d1

-3	5	-11
27225d2	1089a1	27225a1

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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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