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	27048p	Isogeny class
Conductor	27048	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	12394272711066624 = 210 · 34 · 710 · 232	Discriminant
Eigenvalues	2- 3+ -2 7-  0 -6  6  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-66264,3818844]	[a1,a2,a3,a4,a6]
Generators	[230:832:1]	Generators of the group modulo torsion
j	267100692772/102880449	j-invariant
L	3.3872894562846	L(r)(E,1)/r!
Ω	0.36483987987823	Real period
R	4.6421589896027	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	54096u2 81144u2 3864e2	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 27048p2

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

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Quadratic twists for elliptic curve 27048p2

-4	-3	-7
54096u2	81144u2	3864e2

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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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