Cremona's table of elliptic curves

6708 = 2² · 3 · 13 · 43

Field	Data	Notes
Atkin-Lehner	2- 3+ 13+ 43+	Signs for the Atkin-Lehner involutions
Class	6708a	Isogeny class
Conductor	6708	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	8064	Modular degree for the optimal curve
Δ	426439070928 = 24 · 38 · 133 · 432	Discriminant
Eigenvalues	2- 3+  0 -4  2 13+ -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1893,-3654]	[a1,a2,a3,a4,a6]
j	46912110592000/26652441933	j-invariant
L	0.78175004882789	L(r)(E,1)/r!
Ω	0.78175004882789	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	26832q1 107328y1 20124a1 87204b1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 6708a1

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	2	+	-2	4	-4	-6	-10	8	-2	+	10	10	-6	6	2	0	4	-4	-6	-16	2

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Quadratic twists for elliptic curve 6708a1

-4	8	-3	13
26832q1	107328y1	20124a1	87204b1

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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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