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	4048k	Isogeny class
Conductor	4048	Conductor
∏ cp	28	Product of Tamagawa factors cp
deg	55104	Modular degree for the optimal curve
Δ	-797600789912432 = -1 · 24 · 114 · 237	Discriminant
Eigenvalues	2- -1  4 -2 11-  3  6  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-884166,-319707497]	[a1,a2,a3,a4,a6]
j	-4777554520541237119744/49850049369527	j-invariant
L	2.1796854488213	L(r)(E,1)/r!
Ω	0.077845908886476	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	1012a1 16192s1 36432bp1 101200bm1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4048k1

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	4	-2	-	3	6	6	-	-7	-5	-8	7	-4	7	-6	4	10	8	-1	-11	-2	-6	12	14

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Quadratic twists for elliptic curve 4048k1

-4	8	-3	5	-11	-23
1012a1	16192s1	36432bp1	101200bm1	44528s1	93104o1

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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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