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	4048l	Isogeny class
Conductor	4048	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1344	Modular degree for the optimal curve
Δ	132644864 = 219 · 11 · 23	Discriminant
Eigenvalues	2-  2  1  1 11-  3  3  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-760,8304]	[a1,a2,a3,a4,a6]
j	11867954041/32384	j-invariant
L	3.7077232296261	L(r)(E,1)/r!
Ω	1.8538616148131	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	506a1 16192w1 36432bh1 101200bq1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4048l1

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	1	1	-	3	3	6	-	-1	7	-5	-2	8	1	-6	10	-8	-7	5	4	-11	-12	6	2

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Quadratic twists for elliptic curve 4048l1

-4	8	-3	5	-11	-23
506a1	16192w1	36432bh1	101200bq1	44528u1	93104q1

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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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