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	27225bs	Isogeny class
Conductor	27225	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	67200	Modular degree for the optimal curve
Δ	-7845667911675 = -1 · 311 · 52 · 116	Discriminant
Eigenvalues	-2 3- 5+ -3 11-  1 -2  5	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,1815,131436]	[a1,a2,a3,a4,a6]
Generators	[44:544:1]	Generators of the group modulo torsion
j	20480/243	j-invariant
L	2.3933509434239	L(r)(E,1)/r!
Ω	0.54593793130135	Real period
R	1.0959812490583	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	9075n1 27225ca2 225d1	Quadratic twists by: -3 5 -11

Hecke Eigenvalues for elliptic curve 27225bs1

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
-2	-	+	-3	-	1	-2	5	6	10	-3	-2	-8	1	2	-4	10	-7	3	8	-14	0	-6	0	-17

---

Quadratic twists for elliptic curve 27225bs1

-3	5	-11
9075n1	27225ca2	225d1

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations