Cremona's table of elliptic curves

54600 = 2³ · 3 · 5² · 7 · 13

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 7+ 13-	Signs for the Atkin-Lehner involutions
Class	54600cq	Isogeny class
Conductor	54600	Conductor
∏ cp	48	Product of Tamagawa factors cp
deg	319488	Modular degree for the optimal curve
Δ	14590388502144000 = 210 · 32 · 53 · 78 · 133	Discriminant
Eigenvalues	2- 3- 5- 7+  2 13-  0  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-64968,-2639232]	[a1,a2,a3,a4,a6]
Generators	[408:6240:1]	Generators of the group modulo torsion
j	236929380920564/113987410173	j-invariant
L	8.2015384167164	L(r)(E,1)/r!
Ω	0.31370446542083	Real period
R	2.1786796493519	Regulator
r	1	Rank of the group of rational points
S	1.0000000000047	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	109200bk1 54600p1	Quadratic twists by: -4 5

Hecke Eigenvalues for elliptic curve 54600cq1

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

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Quadratic twists for elliptic curve 54600cq1

-4	5
109200bk1	54600p1

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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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