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	6708f	Isogeny class
Conductor	6708	Conductor
∏ cp	36	Product of Tamagawa factors cp
deg	3168	Modular degree for the optimal curve
Δ	-134991792 = -1 · 24 · 33 · 132 · 432	Discriminant
Eigenvalues	2- 3-  2 -4  4 13+ -2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-177,1008]	[a1,a2,a3,a4,a6]
Generators	[-3:39:1]	Generators of the group modulo torsion
j	-38545604608/8436987	j-invariant
L	5.0308942185176	L(r)(E,1)/r!
Ω	1.7640251769637	Real period
R	0.31688223830461	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	26832m1 107328n1 20124b1 87204l1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 6708f1

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
-	-	2	-4	4	+	-2	-8	6	-8	0	10	-8	+	0	-6	-8	-10	12	-10	2	4	-16	2	-2

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Quadratic twists for elliptic curve 6708f1

-4	8	-3	13
26832m1	107328n1	20124b1	87204l1

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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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