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	6188f	Isogeny class
Conductor	6188	Conductor
∏ cp	27	Product of Tamagawa factors cp
deg	3240	Modular degree for the optimal curve
Δ	-350513072 = -1 · 24 · 73 · 13 · 173	Discriminant
Eigenvalues	2-  1  0 7-  3 13- 17- -7	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-3673,84472]	[a1,a2,a3,a4,a6]
Generators	[-69:119:1]	Generators of the group modulo torsion
j	-342597941248000/21907067	j-invariant
L	4.8308813327894	L(r)(E,1)/r!
Ω	1.6167855132879	Real period
R	0.99598478855847	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	24752w1 99008ba1 55692bc1 43316e1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 6188f1

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	0	-	3	-	-	-7	-6	0	8	-7	0	5	-3	-3	0	-10	2	-12	-4	2	-15	-9	-10

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Quadratic twists for elliptic curve 6188f1

-4	8	-3	-7	13	17
24752w1	99008ba1	55692bc1	43316e1	80444c1	105196f1

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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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