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	4048a	Isogeny class
Conductor	4048	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	-44528 = -1 · 24 · 112 · 23	Discriminant
Eigenvalues	2+  1  0  0 11-  1  2 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-8,11]	[a1,a2,a3,a4,a6]
Generators	[5:11:1]	Generators of the group modulo torsion
j	-4000000/2783	j-invariant
L	4.1794453909282	L(r)(E,1)/r!
Ω	3.3172071371194	Real period
R	0.62996448792124	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	2024a1 16192t1 36432c1 101200e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4048a1

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	0	-	1	2	-6	-	-5	1	2	-3	10	-7	-4	-12	-8	14	9	-13	-4	4	10	4

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Quadratic twists for elliptic curve 4048a1

-4	8	-3	5	-11	-23
2024a1	16192t1	36432c1	101200e1	44528f1	93104b1

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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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