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	27075r	Isogeny class
Conductor	27075	Conductor
∏ cp	80	Product of Tamagawa factors cp
deg	345600	Modular degree for the optimal curve
Δ	-322422329606484375 = -1 · 35 · 57 · 198	Discriminant
Eigenvalues	-1 3- 5+  2 -6  0  6 19-	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,171287,1370792]	[a1,a2,a3,a4,a6]
Generators	[353:-10465:1]	Generators of the group modulo torsion
j	756058031/438615	j-invariant
L	4.3218123559272	L(r)(E,1)/r!
Ω	0.1834376336071	Real period
R	1.1780059170366	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	81225bb1 5415c1 1425c1	Quadratic twists by: -3 5 -19

Hecke Eigenvalues for elliptic curve 27075r1

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	-	+	2	-6	0	6	-	8	-4	0	4	0	2	8	2	-12	2	-8	-16	-14	-8	0	0	-12

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Quadratic twists for elliptic curve 27075r1

-3	5	-19
81225bb1	5415c1	1425c1

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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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