Cremona's table of elliptic curves

44 = 2² · 11

Field	Data	Notes
Atkin-Lehner	2- 11+	Signs for the Atkin-Lehner involutions
Class	44a	Isogeny class
Conductor	44	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	2	Modular degree for the optimal curve
Δ	-2816 = -1 · 28 · 11	Discriminant
Eigenvalues	2-  1 -3  2 11+ -4  6  8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,3,-1]	[a1,a2,a3,a4,a6]
j	8192/11	j-invariant
L	0.80464628757465	L(r)(E,1)/r!
Ω	2.413938862724	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	176c1 704d1 396c1 1100a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 44a1

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	-3	2	+	-4	6	8	-3	0	5	-1	0	-10	0	-6	3	-4	-1	15	-4	2	6	-9	-7

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Quadratic twists for elliptic curve 44a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53
176c1	704d1	396c1	1100a1	2156a1	484a1	7436c1	12716d1	15884f1	23276d1	37004b1	42284e1	60236b1	73964d1	81356b1	97196f1	123596a1

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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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