Cremona's table of elliptic curves

4144 = 2⁴ · 7 · 37

Field	Data	Notes
Atkin-Lehner	2+ 7- 37+	Signs for the Atkin-Lehner involutions
Class	4144b	Isogeny class
Conductor	4144	Conductor
∏ cp	7	Product of Tamagawa factors cp
deg	8064	Modular degree for the optimal curve
Δ	-10679020436224 = -1 · 28 · 77 · 373	Discriminant
Eigenvalues	2+  0 -1 7- -5 -1  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-32828,-2294756]	[a1,a2,a3,a4,a6]
j	-15283295882302464/41714923579	j-invariant
L	1.2411820678183	L(r)(E,1)/r!
Ω	0.17731172397404	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	2072d1 16576o1 37296u1 103600g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4144b1

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	-1	6	4	0	0	-5	+	2	-2	2	9	-3	6	-5	-1	10	-4	-14	15	9

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Quadratic twists for elliptic curve 4144b1

-4	8	-3	5	-7
2072d1	16576o1	37296u1	103600g1	29008b1

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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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