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	53361u	Isogeny class
Conductor	53361	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	-1.1869823760656E+22	Discriminant
Eigenvalues	2 3-  2 7+ 11- -1  0 -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-48683019,-130846808997]	[a1,a2,a3,a4,a6]
Generators	[69211427082578549241908801212:2758446457007837769572602886735:7860375619229852220681152]	Generators of the group modulo torsion
j	-1713910976512/1594323	j-invariant
L	14.259887157933	L(r)(E,1)/r!
Ω	0.028575968479159	Real period
R	41.584729864691	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	17787m2 53361bt2 441e2	Quadratic twists by: -3 -7 -11

Hecke Eigenvalues for elliptic curve 53361u2

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	+	-	-1	0	-1	0	4	9	3	-10	-5	6	-12	12	-10	-5	6	3	1	6	-16	-6

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Quadratic twists for elliptic curve 53361u2

-3	-7	-11
17787m2	53361bt2	441e2

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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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