Cremona's table of elliptic curves

6728 = 2³ · 29²

Field	Data	Notes
Atkin-Lehner	2+ 29+	Signs for the Atkin-Lehner involutions
Class	6728a	Isogeny class
Conductor	6728	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	13440	Modular degree for the optimal curve
Δ	-17663873340416 = -1 · 210 · 297	Discriminant
Eigenvalues	2+ -1  1  2 -3 -1  0  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-67560,-6739556]	[a1,a2,a3,a4,a6]
Generators	[36666:7020668:1]	Generators of the group modulo torsion
j	-55990084/29	j-invariant
L	3.6165723480485	L(r)(E,1)/r!
Ω	0.14805842356963	Real period
R	6.1066642830149	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	13456a1 53824a1 60552o1 232b1	Quadratic twists by: -4 8 -3 29

Hecke Eigenvalues for elliptic curve 6728a1

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	1	2	-3	-1	0	0	4	+	-3	8	6	5	-3	5	-8	0	-12	6	4	-1	-12	-6	-14

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Quadratic twists for elliptic curve 6728a1

-4	8	-3	29
13456a1	53824a1	60552o1	232b1

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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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