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	27225bi	Isogeny class
Conductor	27225	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	61440	Modular degree for the optimal curve
Δ	-302687805234375 = -1 · 37 · 57 · 116	Discriminant
Eigenvalues	1 3- 5+  0 11- -2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-567,837216]	[a1,a2,a3,a4,a6]
Generators	[-36:918:1]	Generators of the group modulo torsion
j	-1/15	j-invariant
L	5.7394728102493	L(r)(E,1)/r!
Ω	0.43614719585814	Real period
R	1.644935719166	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	9075l1 5445g1 225c1	Quadratic twists by: -3 5 -11

Hecke Eigenvalues for elliptic curve 27225bi1

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

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Quadratic twists for elliptic curve 27225bi1

-3	5	-11
9075l1	5445g1	225c1

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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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