Cremona's table of elliptic curves

6727 = 7 · 31²

Field	Data	Notes
Atkin-Lehner	7+ 31-	Signs for the Atkin-Lehner involutions
Class	6727a	Isogeny class
Conductor	6727	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	53568	Modular degree for the optimal curve
Δ	9068790401110153 = 73 · 319	Discriminant
Eigenvalues	1  0  2 7+  6  6 -6  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-202951,-34841040]	[a1,a2,a3,a4,a6]
j	34965783/343	j-invariant
L	2.8133183942795	L(r)(E,1)/r!
Ω	0.22506547154236	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	25	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	107632m1 60543j1 47089b1 6727b1	Quadratic twists by: -4 -3 -7 -31

Hecke Eigenvalues for elliptic curve 6727a1

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	0	2	+	6	6	-6	0	6	0	-	0	10	-6	-4	-12	4	6	12	-8	-6	6	12	-6	-10

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Quadratic twists for elliptic curve 6727a1

-4	-3	-7	-31
107632m1	60543j1	47089b1	6727b1

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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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