Cremona's table of elliptic curves

1044 = 2² · 3² · 29

Field	Data	Notes
Atkin-Lehner	2- 3+ 29+	Signs for the Atkin-Lehner involutions
Class	1044b	Isogeny class
Conductor	1044	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	288	Modular degree for the optimal curve
Δ	-9132912 = -1 · 24 · 39 · 29	Discriminant
Eigenvalues	2- 3+  4  1 -3  5  5 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,27,-135]	[a1,a2,a3,a4,a6]
j	6912/29	j-invariant
L	2.3374739375833	L(r)(E,1)/r!
Ω	1.1687369687916	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	4176r1 16704n1 1044d1 26100b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1044b1

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
-	+	4	1	-3	5	5	-6	4	+	-6	-10	2	-2	13	-2	6	-8	15	-10	4	0	-8	-1	-2

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Quadratic twists for elliptic curve 1044b1

-4	8	-3	5	-7	-11	29
4176r1	16704n1	1044d1	26100b1	51156b1	126324d1	30276e1

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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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