Cremona's table of elliptic curves

6137 = 17 · 19²

Field	Data	Notes
Atkin-Lehner	17- 19-	Signs for the Atkin-Lehner involutions
Class	6137b	Isogeny class
Conductor	6137	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	799779977 = 17 · 196	Discriminant
Eigenvalues	1  0 -2  4  0  2 17- 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-32738,2288159]	[a1,a2,a3,a4,a6]
Generators	[11930:14251:125]	Generators of the group modulo torsion
j	82483294977/17	j-invariant
L	4.5032717448857	L(r)(E,1)/r!
Ω	1.2598315095873	Real period
R	3.5745031860338	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	98192v4 55233g4 104329d4 17a3	Quadratic twists by: -4 -3 17 -19

Hecke Eigenvalues for elliptic curve 6137b3

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	-2	4	0	2	-	-	4	-6	-4	2	6	4	0	-6	12	-10	-4	4	-6	-12	-4	-10	-2

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Quadratic twists for elliptic curve 6137b3

-4	-3	17	-19
98192v4	55233g4	104329d4	17a3

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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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