Cremona's table of elliptic curves

53361 = 3² · 7² · 11²

Field	Data	Notes
Atkin-Lehner	3- 7+ 11-	Signs for the Atkin-Lehner involutions
Class	53361s	Isogeny class
Conductor	53361	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	138240	Modular degree for the optimal curve
Δ	-102326881587777 = -1 · 37 · 74 · 117	Discriminant
Eigenvalues	1 3-  0 7+ 11- -4  3 -1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-27792,-1841603]	[a1,a2,a3,a4,a6]
Generators	[10916:1134869:1]	Generators of the group modulo torsion
j	-765625/33	j-invariant
L	6.0548327297875	L(r)(E,1)/r!
Ω	0.18441454952985	Real period
R	8.208181980744	Regulator
r	1	Rank of the group of rational points
S	1.0000000000059	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	17787b1 53361be1 4851h1	Quadratic twists by: -3 -7 -11

Hecke Eigenvalues for elliptic curve 53361s1

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
1	-	0	+	-	-4	3	-1	1	-5	-10	-11	10	3	9	8	9	2	4	7	-4	8	8	0	-1

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Quadratic twists for elliptic curve 53361s1

-3	-7	-11
17787b1	53361be1	4851h1

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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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