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	6710f	Isogeny class
Conductor	6710	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	225120500 = 22 · 53 · 112 · 612	Discriminant
Eigenvalues	2-  0 5+ -4 11- -4 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-2653,-51919]	[a1,a2,a3,a4,a6]
j	2064343598432289/225120500	j-invariant
L	1.3304877167805	L(r)(E,1)/r!
Ω	0.66524385839026	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	53680o2 60390o2 33550d2 73810b2	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 6710f2

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

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Quadratic twists for elliptic curve 6710f2

-4	-3	5	-11
53680o2	60390o2	33550d2	73810b2

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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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