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	6688b	Isogeny class
Conductor	6688	Conductor
∏ cp	12	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]
Generators	[-12:22:1] [12:-38:1]	Generators of the group modulo torsion
j	-245314376/829939	j-invariant
L	4.0804712238	L(r)(E,1)/r!
Ω	1.4700811966747	Real period
R	0.23130645396947	Regulator
r	2	Rank of the group of rational points
S	0.99999999999997	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	6688c1 13376r1 60192z1 73568q1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 6688b1

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 6688b1

-4	8	-3	-11	-19
6688c1	13376r1	60192z1	73568q1	127072q1

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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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