Cremona's table of elliptic curves

6728 = 2³ · 29²

Field	Data	Notes
Atkin-Lehner	2- 29+	Signs for the Atkin-Lehner involutions
Class	6728c	Isogeny class
Conductor	6728	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	840	Modular degree for the optimal curve
Δ	-1722368 = -1 · 211 · 292	Discriminant
Eigenvalues	2-  1  0 -4 -3 -2 -2  3	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-48,-160]	[a1,a2,a3,a4,a6]
j	-7250	j-invariant
L	0.89844566016862	L(r)(E,1)/r!
Ω	0.89844566016862	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	13456b1 53824c1 60552f1 6728b1	Quadratic twists by: -4 8 -3 29

Hecke Eigenvalues for elliptic curve 6728c1

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	-4	-3	-2	-2	3	-6	+	0	-8	11	11	4	6	4	0	0	-10	10	12	11	-11	11

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Quadratic twists for elliptic curve 6728c1

-4	8	-3	29
13456b1	53824c1	60552f1	6728b1

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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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