Cremona's table of elliptic curves

6699 = 3 · 7 · 11 · 29

Field	Data	Notes
Atkin-Lehner	3+ 7+ 11- 29-	Signs for the Atkin-Lehner involutions
Class	6699d	Isogeny class
Conductor	6699	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	216318148151991039 = 324 · 74 · 11 · 29	Discriminant
Eigenvalues	-1 3+ -2 7+ 11-  2  2 -8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-544214,152670836]	[a1,a2,a3,a4,a6]
Generators	[2990:8791:8]	Generators of the group modulo torsion
j	17825137625614555960417/216318148151991039	j-invariant
L	1.6479495133507	L(r)(E,1)/r!
Ω	0.31664230011643	Real period
R	5.20445156173	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	107184ct3 20097f4 46893r3 73689m3	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 6699d3

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

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Quadratic twists for elliptic curve 6699d3

-4	-3	-7	-11
107184ct3	20097f4	46893r3	73689m3

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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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