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	5733b	Isogeny class
Conductor	5733	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	289063593 = 33 · 77 · 13	Discriminant
Eigenvalues	-1 3+  0 7-  0 13- -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-230,-1004]	[a1,a2,a3,a4,a6]
Generators	[-8:20:1]	Generators of the group modulo torsion
j	421875/91	j-invariant
L	2.5000806193343	L(r)(E,1)/r!
Ω	1.2451271708104	Real period
R	2.0078917864326	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	91728ct1 5733a1 819b1 74529i1	Quadratic twists by: -4 -3 -7 13

Hecke Eigenvalues for elliptic curve 5733b1

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	-	0	-	-2	4	6	-4	0	-10	-12	-4	10	-12	14	10	0	8	-2	0	6	0	2

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Quadratic twists for elliptic curve 5733b1

-4	-3	-7	13
91728ct1	5733a1	819b1	74529i1

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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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