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	6688a	Isogeny class
Conductor	6688	Conductor
∏ cp	8	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]
Generators	[460635:3531302:3375]	Generators of the group modulo torsion
j	-128894765196744/639533521	j-invariant
L	4.2327950892084	L(r)(E,1)/r!
Ω	0.24912972360387	Real period
R	8.4951627368616	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	6688d2 13376i2 60192v2 73568s2	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 6688a2

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 6688a2

-4	8	-3	-11	-19
6688d2	13376i2	60192v2	73568s2	127072o2

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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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