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	54450ef	Isogeny class
Conductor	54450	Conductor
∏ cp	200	Product of Tamagawa factors cp
deg	1382400	Modular degree for the optimal curve
Δ	6243334225920000000 = 225 · 39 · 57 · 112	Discriminant
Eigenvalues	2- 3+ 5+  3 11- -3 -1 -5	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-1712855,854849647]	[a1,a2,a3,a4,a6]
Generators	[2179:-87490:1]	Generators of the group modulo torsion
j	14934427706187/167772160	j-invariant
L	10.586377620902	L(r)(E,1)/r!
Ω	0.23935237175426	Real period
R	0.22114628619046	Regulator
r	1	Rank of the group of rational points
S	1.0000000000033	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	54450m1 10890i1 54450n1	Quadratic twists by: -3 5 -11

Hecke Eigenvalues for elliptic curve 54450ef1

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

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Quadratic twists for elliptic curve 54450ef1

-3	5	-11
54450m1	10890i1	54450n1

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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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