Cremona's table of elliptic curves

27360 = 2⁵ · 3² · 5 · 19

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 19-	Signs for the Atkin-Lehner involutions
Class	27360x	Isogeny class
Conductor	27360	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	319127040000 = 212 · 38 · 54 · 19	Discriminant
Eigenvalues	2- 3- 5+  0 -4 -2 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-8508,300832]	[a1,a2,a3,a4,a6]
Generators	[62:-108:1] [-91:567:1]	Generators of the group modulo torsion
j	22809653056/106875	j-invariant
L	7.6452607533895	L(r)(E,1)/r!
Ω	0.97082887490451	Real period
R	0.98437285795386	Regulator
r	2	Rank of the group of rational points
S	0.99999999999979	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	27360g3 54720bo1 9120j2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 27360x3

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

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Quadratic twists for elliptic curve 27360x3

-4	8	-3
27360g3	54720bo1	9120j2

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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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