Cremona's table of elliptic curves

4048 = 2⁴ · 11 · 23

Field	Data	Notes
Atkin-Lehner	2- 11+ 23-	Signs for the Atkin-Lehner involutions
Class	4048g	Isogeny class
Conductor	4048	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	4385570816 = 215 · 11 · 233	Discriminant
Eigenvalues	2-  2  3 -5 11+ -1 -3 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-6344,196592]	[a1,a2,a3,a4,a6]
Generators	[34:138:1]	Generators of the group modulo torsion
j	6894801108937/1070696	j-invariant
L	5.0237626277932	L(r)(E,1)/r!
Ω	1.3347927664003	Real period
R	0.62728371952218	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	506c2 16192bf2 36432ci2 101200ba2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4048g2

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
-	2	3	-5	+	-1	-3	-2	-	3	-5	-7	-6	-8	-3	6	6	8	7	9	-16	-17	-12	6	-10

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Quadratic twists for elliptic curve 4048g2

-4	8	-3	5	-11	-23
506c2	16192bf2	36432ci2	101200ba2	44528y2	93104bf2

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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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