Cremona's table of elliptic curves

9048 = 2³ · 3 · 13 · 29

Field	Data	Notes
Atkin-Lehner	2- 3- 13- 29+	Signs for the Atkin-Lehner involutions
Class	9048n	Isogeny class
Conductor	9048	Conductor
∏ cp	288	Product of Tamagawa factors cp
Δ	251374416014592 = 28 · 312 · 133 · 292	Discriminant
Eigenvalues	2- 3- -2 -4 -6 13- -6 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-18764,623760]	[a1,a2,a3,a4,a6]
Generators	[-128:972:1] [-110:1170:1]	Generators of the group modulo torsion
j	2854191868572112/981931312557	j-invariant
L	5.6113455178119	L(r)(E,1)/r!
Ω	0.50932830227961	Real period
R	0.15301595074384	Regulator
r	2	Rank of the group of rational points
S	0.99999999999995	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	18096g2 72384i2 27144f2 117624o2	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 9048n2

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	-4	-6	-	-6	-6	-8	+	-6	4	0	4	-6	2	-8	6	12	-12	-4	-8	0	0	-4

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Quadratic twists for elliptic curve 9048n2

-4	8	-3	13
18096g2	72384i2	27144f2	117624o2

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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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