Cremona's table of elliptic curves

27048 = 2³ · 3 · 7² · 23

Field	Data	Notes
Atkin-Lehner	2+ 3- 7- 23+	Signs for the Atkin-Lehner involutions
Class	27048h	Isogeny class
Conductor	27048	Conductor
∏ cp	168	Product of Tamagawa factors cp
deg	1919232	Modular degree for the optimal curve
Δ	-2.4854012394E+21	Discriminant
Eigenvalues	2+ 3- -4 7- -1  0 -6 -1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-3312465,-3338439021]	[a1,a2,a3,a4,a6]
Generators	[3495:-166698:1]	Generators of the group modulo torsion
j	-389094786976768/240588123669	j-invariant
L	4.3047329384219	L(r)(E,1)/r!
Ω	0.054425195100658	Real period
R	0.47080052355089	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	54096l1 81144cd1 27048b1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 27048h1

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
+	-	-4	-	-1	0	-6	-1	+	4	6	-8	9	-10	1	3	3	-7	0	10	-4	8	14	14	-2

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Quadratic twists for elliptic curve 27048h1

-4	-3	-7
54096l1	81144cd1	27048b1

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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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