Cremona's table of elliptic curves

6710 = 2 · 5 · 11 · 61

Field	Data	Notes
Atkin-Lehner	2- 5- 11- 61-	Signs for the Atkin-Lehner involutions
Class	6710i	Isogeny class
Conductor	6710	Conductor
∏ cp	20	Product of Tamagawa factors cp
deg	3840	Modular degree for the optimal curve
Δ	13420000 = 25 · 54 · 11 · 61	Discriminant
Eigenvalues	2- -3 5-  0 11- -5  7 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-72,171]	[a1,a2,a3,a4,a6]
Generators	[1:9:1]	Generators of the group modulo torsion
j	40743095121/13420000	j-invariant
L	3.957807075088	L(r)(E,1)/r!
Ω	2.06242207194	Real period
R	0.095950463509271	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	53680be1 60390g1 33550j1 73810g1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 6710i1

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
-	-3	-	0	-	-5	7	-4	-4	0	-7	11	0	3	-10	9	-14	-	-4	-1	-16	10	4	-2	-1

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Quadratic twists for elliptic curve 6710i1

-4	-3	5	-11
53680be1	60390g1	33550j1	73810g1

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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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