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	54450eg	Isogeny class
Conductor	54450	Conductor
∏ cp	300	Product of Tamagawa factors cp
deg	5068800	Modular degree for the optimal curve
Δ	1.5172081515233E+22	Discriminant
Eigenvalues	2- 3+ 5+ -3 11-  3 -1  5	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-23028380,42125569247]	[a1,a2,a3,a4,a6]
Generators	[-2571:291685:1]	Generators of the group modulo torsion
j	14934427706187/167772160	j-invariant
L	8.7119254814449	L(r)(E,1)/r!
Ω	0.12499769946725	Real period
R	0.23232228855782	Regulator
r	1	Rank of the group of rational points
S	1.0000000000042	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	54450n1 10890d1 54450m1	Quadratic twists by: -3 5 -11

Hecke Eigenvalues for elliptic curve 54450eg1

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	-	3	-1	5	-6	1	0	-9	4	-4	4	2	-8	4	-8	5	4	4	15	-6	12

---

Quadratic twists for elliptic curve 54450eg1

-3	5	-11
54450n1	10890d1	54450m1

---

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