Cremona's table of elliptic curves

6643 = 7 · 13 · 73

Field	Data	Notes
Atkin-Lehner	7+ 13+ 73-	Signs for the Atkin-Lehner involutions
Class	6643a	Isogeny class
Conductor	6643	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	8232	Modular degree for the optimal curve
Δ	-4164838954003 = -1 · 77 · 13 · 733	Discriminant
Eigenvalues	1  0  0 7+ -3 13+ -5 -1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-6347,-216412]	[a1,a2,a3,a4,a6]
j	-28279237523279625/4164838954003	j-invariant
L	0.79583404465154	L(r)(E,1)/r!
Ω	0.26527801488385	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	106288q1 59787e1 46501d1 86359a1	Quadratic twists by: -4 -3 -7 13

Hecke Eigenvalues for elliptic curve 6643a1

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	0	+	-3	+	-5	-1	9	-2	0	-10	-6	-4	10	-6	8	2	6	-2	-	15	-6	-15	1

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Quadratic twists for elliptic curve 6643a1

-4	-3	-7	13
106288q1	59787e1	46501d1	86359a1

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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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