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	53361x	Isogeny class
Conductor	53361	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	358848	Modular degree for the optimal curve
Δ	-184588161301467 = -1 · 37 · 78 · 114	Discriminant
Eigenvalues	-2 3-  2 7+ 11- -3 -2  1	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-124509,16922848]	[a1,a2,a3,a4,a6]
Generators	[196:-221:1]	Generators of the group modulo torsion
j	-3469312/3	j-invariant
L	3.1175455002414	L(r)(E,1)/r!
Ω	0.56471455946794	Real period
R	0.46004738854075	Regulator
r	1	Rank of the group of rational points
S	0.99999999999724	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	17787d1 53361cc1 53361v1	Quadratic twists by: -3 -7 -11

Hecke Eigenvalues for elliptic curve 53361x1

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	-	2	+	-	-3	-2	1	-6	2	-4	-6	-4	11	8	6	14	-1	15	-6	-10	7	-4	-6	-7

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Quadratic twists for elliptic curve 53361x1

-3	-7	-11
17787d1	53361cc1	53361v1

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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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