Cremona's table of elliptic curves

54450 = 2 · 3² · 5² · 11²

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 11-	Signs for the Atkin-Lehner involutions
Class	54450gc	Isogeny class
Conductor	54450	Conductor
∏ cp	160	Product of Tamagawa factors cp
deg	1152000	Modular degree for the optimal curve
Δ	-88373603357107200 = -1 · 210 · 311 · 52 · 117	Discriminant
Eigenvalues	2- 3- 5+ -3 11- -4 -7 -5	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-983390,375868397]	[a1,a2,a3,a4,a6]
Generators	[465:-4589:1] [-15:19771:1]	Generators of the group modulo torsion
j	-3257444411545/2737152	j-invariant
L	13.155542132562	L(r)(E,1)/r!
Ω	0.3375507547609	Real period
R	0.24358451927251	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	18150bg1 54450dk2 4950k1	Quadratic twists by: -3 5 -11

Hecke Eigenvalues for elliptic curve 54450gc1

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
-	-	+	-3	-	-4	-7	-5	1	-10	2	-7	-3	-4	-13	-4	5	-12	-12	3	-4	15	14	0	-7

---

Quadratic twists for elliptic curve 54450gc1

-3	5	-11
18150bg1	54450dk2	4950k1

---

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