Cremona's table of elliptic curves

27075 = 3 · 5² · 19²

Field	Data	Notes
Atkin-Lehner	3- 5+ 19+	Signs for the Atkin-Lehner involutions
Class	27075m	Isogeny class
Conductor	27075	Conductor
∏ cp	14	Product of Tamagawa factors cp
Δ	-580360193291671875 = -1 · 37 · 56 · 198	Discriminant
Eigenvalues	-1 3- 5+ -1 -2 -5  4 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-5983763,-5634525108]	[a1,a2,a3,a4,a6]
j	-89289015625/2187	j-invariant
L	0.67569913051318	L(r)(E,1)/r!
Ω	0.048264223608087	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	81225r2 1083a2 27075d2	Quadratic twists by: -3 5 -19

Hecke Eigenvalues for elliptic curve 27075m2

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
-1	-	+	-1	-2	-5	4	+	4	-8	-3	-3	-12	1	6	-4	10	-13	-11	6	11	1	0	-6	-2

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Quadratic twists for elliptic curve 27075m2

-3	5	-19
81225r2	1083a2	27075d2

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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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