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	6188b	Isogeny class
Conductor	6188	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1344	Modular degree for the optimal curve
Δ	8489936 = 24 · 74 · 13 · 17	Discriminant
Eigenvalues	2-  2  2 7+ -4 13- 17+ -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-57,110]	[a1,a2,a3,a4,a6]
Generators	[-470:2004:125]	Generators of the group modulo torsion
j	1302642688/530621	j-invariant
L	5.8319743133092	L(r)(E,1)/r!
Ω	2.1069730721286	Real period
R	5.5358793052039	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	24752bc1 99008d1 55692x1 43316m1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 6188b1

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	2	+	-4	-	+	-2	6	-6	-8	-6	-6	-8	-10	-2	-6	-2	14	8	10	2	14	6	10

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Quadratic twists for elliptic curve 6188b1

-4	8	-3	-7	13	17
24752bc1	99008d1	55692x1	43316m1	80444e1	105196n1

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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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