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	4048d	Isogeny class
Conductor	4048	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	264	Modular degree for the optimal curve
Δ	-93104 = -1 · 24 · 11 · 232	Discriminant
Eigenvalues	2-  0  2 -4 11+  2  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-4,15]	[a1,a2,a3,a4,a6]
j	-442368/5819	j-invariant
L	1.43491797182	L(r)(E,1)/r!
Ω	2.86983594364	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1012d1 16192y1 36432cu1 101200bd1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4048d1

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	2	-4	+	2	0	-4	+	6	8	-2	2	4	4	6	-4	-4	-4	-8	14	16	0	10	-2

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Quadratic twists for elliptic curve 4048d1

-4	8	-3	5	-11	-23
1012d1	16192y1	36432cu1	101200bd1	44528l1	93104w1

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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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