Cremona's table of elliptic curves

4944 = 2⁴ · 3 · 103

Field	Data	Notes
Atkin-Lehner	2- 3+ 103-	Signs for the Atkin-Lehner involutions
Class	4944g	Isogeny class
Conductor	4944	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	480	Modular degree for the optimal curve
Δ	-79104 = -1 · 28 · 3 · 103	Discriminant
Eigenvalues	2- 3+ -1  4  0  3 -4  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,4,12]	[a1,a2,a3,a4,a6]
Generators	[1:4:1]	Generators of the group modulo torsion
j	21296/309	j-invariant
L	3.4792284578174	L(r)(E,1)/r!
Ω	2.5448340854896	Real period
R	1.3671730026156	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	1236b1 19776bf1 14832o1 123600bz1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4944g1

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	4	0	3	-4	0	-7	-8	9	-4	-6	9	4	-10	-3	-13	-13	-12	-10	-4	9	18	13

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Quadratic twists for elliptic curve 4944g1

-4	8	-3	5
1236b1	19776bf1	14832o1	123600bz1

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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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