Cremona's table of elliptic curves

6137 = 17 · 19²

Field	Data	Notes
Atkin-Lehner	17+ 19-	Signs for the Atkin-Lehner involutions
Class	6137a	Isogeny class
Conductor	6137	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	50400	Modular degree for the optimal curve
Δ	-1269170045721323 = -1 · 175 · 197	Discriminant
Eigenvalues	0 -3 -2  4 -2 -6 17+ 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-16606,-1901658]	[a1,a2,a3,a4,a6]
j	-10764582912/26977283	j-invariant
L	0.39169660392994	L(r)(E,1)/r!
Ω	0.19584830196497	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	98192s1 55233o1 104329c1 323a1	Quadratic twists by: -4 -3 17 -19

Hecke Eigenvalues for elliptic curve 6137a1

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
0	-3	-2	4	-2	-6	+	-	0	9	9	-2	6	-1	-3	-2	-14	-6	14	-16	-2	-8	-3	-2	7

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Quadratic twists for elliptic curve 6137a1

-4	-3	17	-19
98192s1	55233o1	104329c1	323a1

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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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