Cremona's table of elliptic curves

5733 = 3² · 7² · 13

Field	Data	Notes
Atkin-Lehner	3- 7+ 13+	Signs for the Atkin-Lehner involutions
Class	5733d	Isogeny class
Conductor	5733	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-109830549012093 = -1 · 36 · 74 · 137	Discriminant
Eigenvalues	-1 3-  0 7+  3 13+ -7 -7	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,5650,475570]	[a1,a2,a3,a4,a6]
j	11397810375/62748517	j-invariant
L	0.85663718194049	L(r)(E,1)/r!
Ω	0.42831859097025	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	91728df2 637a2 5733k2 74529m2	Quadratic twists by: -4 -3 -7 13

Hecke Eigenvalues for elliptic curve 5733d2

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	+	3	+	-7	-7	6	5	0	8	0	2	-7	3	7	-7	-3	5	14	-6	0	0	-14

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Quadratic twists for elliptic curve 5733d2

-4	-3	-7	13
91728df2	637a2	5733k2	74529m2

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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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