Cremona's table of elliptic curves

6688 = 2⁵ · 11 · 19

Field	Data	Notes
Atkin-Lehner	2- 11- 19-	Signs for the Atkin-Lehner involutions
Class	6688d	Isogeny class
Conductor	6688	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	-327441162752 = -1 · 29 · 116 · 192	Discriminant
Eigenvalues	2-  0  2  2 11-  2  6 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-8419,298602]	[a1,a2,a3,a4,a6]
j	-128894765196744/639533521	j-invariant
L	2.9065474459639	L(r)(E,1)/r!
Ω	0.96884914865464	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	6688a2 13376b2 60192e2 73568d2	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 6688d2

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

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Quadratic twists for elliptic curve 6688d2

-4	8	-3	-11	-19
6688a2	13376b2	60192e2	73568d2	127072j2

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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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