Cremona's table of elliptic curves

6188 = 2² · 7 · 13 · 17

Field	Data	Notes
Atkin-Lehner	2- 7- 13+ 17+	Signs for the Atkin-Lehner involutions
Class	6188d	Isogeny class
Conductor	6188	Conductor
∏ cp	10	Product of Tamagawa factors cp
deg	21600	Modular degree for the optimal curve
Δ	-789506859791104 = -1 · 28 · 75 · 133 · 174	Discriminant
Eigenvalues	2- -2 -1 7-  0 13+ 17+ -3	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-26341,-2138409]	[a1,a2,a3,a4,a6]
Generators	[602:14161:1]	Generators of the group modulo torsion
j	-7895815816413184/3084011171059	j-invariant
L	2.5444833392492	L(r)(E,1)/r!
Ω	0.18382017332598	Real period
R	1.3842242084806	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	24752r1 99008bh1 55692z1 43316s1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 6188d1

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
-	-2	-1	-	0	+	+	-3	5	-1	9	-2	-2	1	-5	3	8	10	2	-14	-11	-15	-9	13	9

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Quadratic twists for elliptic curve 6188d1

-4	8	-3	-7	13	17
24752r1	99008bh1	55692z1	43316s1	80444b1	105196b1

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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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