Cremona's table of elliptic curves

6027 = 3 · 7² · 41

Field	Data	Notes
Atkin-Lehner	3- 7+ 41+	Signs for the Atkin-Lehner involutions
Class	6027f	Isogeny class
Conductor	6027	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	20832	Modular degree for the optimal curve
Δ	-29071891443 = -1 · 3 · 78 · 412	Discriminant
Eigenvalues	2 3-  0 7+  4 -1  4  7	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-54308,4853237]	[a1,a2,a3,a4,a6]
j	-3072832000000/5043	j-invariant
L	6.0409373679885	L(r)(E,1)/r!
Ω	1.0068228946647	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	96432t1 18081g1 6027e1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 6027f1

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	-	0	+	4	-1	4	7	6	-8	1	7	+	-7	0	4	8	2	13	-6	1	-7	8	14	-2

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Quadratic twists for elliptic curve 6027f1

-4	-3	-7
96432t1	18081g1	6027e1

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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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