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	6688c	Isogeny class
Conductor	6688	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1728	Modular degree for the optimal curve
Δ	-424928768 = -1 · 29 · 112 · 193	Discriminant
Eigenvalues	2+  1 -2  1 11- -5 -3 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-104,-1108]	[a1,a2,a3,a4,a6]
j	-245314376/829939	j-invariant
L	1.3735727027379	L(r)(E,1)/r!
Ω	0.68678635136897	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	6688b1 13376p1 60192m1 73568u1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 6688c1

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	1	-	-5	-3	+	3	-5	2	6	-10	12	8	9	13	0	5	2	-1	8	-4	8	-16

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Quadratic twists for elliptic curve 6688c1

-4	8	-3	-11	-19
6688b1	13376p1	60192m1	73568u1	127072x1

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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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