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	4048j	Isogeny class
Conductor	4048	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	-651934448 = -1 · 24 · 116 · 23	Discriminant
Eigenvalues	2- -1  0  4 11-  5 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2278,42635]	[a1,a2,a3,a4,a6]
Generators	[29:11:1]	Generators of the group modulo torsion
j	-81743931616000/40745903	j-invariant
L	3.4102660129424	L(r)(E,1)/r!
Ω	1.5960010547134	Real period
R	0.35612612356687	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	1012b2 16192q2 36432bs2 101200bw2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4048j2

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	0	4	-	5	-6	-2	+	-9	-5	-10	-3	10	3	0	-12	-4	-2	3	11	-8	0	6	8

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Quadratic twists for elliptic curve 4048j2

-4	8	-3	5	-11	-23
1012b2	16192q2	36432bs2	101200bw2	44528p2	93104l2

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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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