Cremona's table of elliptic curves

27040 = 2⁵ · 5 · 13²

Field	Data	Notes
Atkin-Lehner	2+ 5+ 13+	Signs for the Atkin-Lehner involutions
Class	27040a	Isogeny class
Conductor	27040	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	34944	Modular degree for the optimal curve
Δ	-2088270645760 = -1 · 29 · 5 · 138	Discriminant
Eigenvalues	2+  0 5+ -1  5 13+  4  7	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,2197,57122]	[a1,a2,a3,a4,a6]
Generators	[-12166:253508:1331]	Generators of the group modulo torsion
j	2808/5	j-invariant
L	5.053861855821	L(r)(E,1)/r!
Ω	0.56681541904282	Real period
R	8.9162391953899	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	27040o1 54080bd1 27040r1	Quadratic twists by: -4 8 13

Hecke Eigenvalues for elliptic curve 27040a1

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
+	0	+	-1	5	+	4	7	-4	8	-6	-7	-10	2	-3	-3	4	-6	-8	14	4	-10	4	1	-12

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Quadratic twists for elliptic curve 27040a1

-4	8	13
27040o1	54080bd1	27040r1

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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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