Cremona's table of elliptic curves

1533 = 3 · 7 · 73

Field	Data	Notes
Atkin-Lehner	3- 7+ 73-	Signs for the Atkin-Lehner involutions
Class	1533b	Isogeny class
Conductor	1533	Conductor
∏ cp	18	Product of Tamagawa factors cp
deg	576	Modular degree for the optimal curve
Δ	-3449898459 = -1 · 39 · 74 · 73	Discriminant
Eigenvalues	0 3- -1 7+  0  4  1 -5	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-231,-3211]	[a1,a2,a3,a4,a6]
Generators	[39:220:1]	Generators of the group modulo torsion
j	-1369110052864/3449898459	j-invariant
L	2.6430571339065	L(r)(E,1)/r!
Ω	0.56994129614806	Real period
R	0.25763444135676	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	24528l1 98112h1 4599c1 38325b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1533b1

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
0	-	-1	+	0	4	1	-5	-6	6	-6	1	4	-10	-9	-9	-11	3	3	-8	-	-5	-3	-2	-7

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Quadratic twists for elliptic curve 1533b1

-4	8	-3	5	-7	73
24528l1	98112h1	4599c1	38325b1	10731a1	111909g1

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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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