Cremona's table of elliptic curves

27104 = 2⁵ · 7 · 11²

Field	Data	Notes
Atkin-Lehner	2+ 7- 11-	Signs for the Atkin-Lehner involutions
Class	27104i	Isogeny class
Conductor	27104	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	23040	Modular degree for the optimal curve
Δ	-96032778688 = -1 · 26 · 7 · 118	Discriminant
Eigenvalues	2+ -2 -2 7- 11- -4  0  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,686,13440]	[a1,a2,a3,a4,a6]
Generators	[29:242:1]	Generators of the group modulo torsion
j	314432/847	j-invariant
L	2.3847088901735	L(r)(E,1)/r!
Ω	0.74854753030209	Real period
R	1.5928907608653	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	27104n1 54208bk2 2464k1	Quadratic twists by: -4 8 -11

Hecke Eigenvalues for elliptic curve 27104i1

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

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Quadratic twists for elliptic curve 27104i1

-4	8	-11
27104n1	54208bk2	2464k1

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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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