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	1044a	Isogeny class
Conductor	1044	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	1440	Modular degree for the optimal curve
Δ	-6459535132272 = -1 · 24 · 39 · 295	Discriminant
Eigenvalues	2- 3+  0  1  5 -3  5 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-3105,-139239]	[a1,a2,a3,a4,a6]
j	-10512288000/20511149	j-invariant
L	1.8045178479463	L(r)(E,1)/r!
Ω	0.30075297465772	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	4176n1 16704h1 1044c1 26100c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1044a1

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

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Quadratic twists for elliptic curve 1044a1

-4	8	-3	5	-7	-11	29
4176n1	16704h1	1044c1	26100c1	51156a1	126324c1	30276b1

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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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