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	53361by	Isogeny class
Conductor	53361	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	1197504	Modular degree for the optimal curve
Δ	-496387702582306227 = -1 · 39 · 76 · 118	Discriminant
Eigenvalues	2 3-  4 7- 11-  2  4  3	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,195657,-6277329]	[a1,a2,a3,a4,a6]
j	45056/27	j-invariant
L	9.2640855120742	L(r)(E,1)/r!
Ω	0.17155713912889	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	9	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	17787bg1 1089i1 53361cg1	Quadratic twists by: -3 -7 -11

Hecke Eigenvalues for elliptic curve 53361by1

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	-	4	-	-	2	4	3	-2	-6	5	3	-2	12	2	-6	-10	-3	-1	0	11	11	6	12	-5

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Quadratic twists for elliptic curve 53361by1

-3	-7	-11
17787bg1	1089i1	53361cg1

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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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