Cremona's table of elliptic curves

6083 = 7 · 11 · 79

Field	Data	Notes
Atkin-Lehner	7+ 11+ 79+	Signs for the Atkin-Lehner involutions
Class	6083a	Isogeny class
Conductor	6083	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	3440	Modular degree for the optimal curve
Δ	-12691990927 = -1 · 75 · 112 · 792	Discriminant
Eigenvalues	1  2  2 7+ 11+  0 -2 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,61,-5392]	[a1,a2,a3,a4,a6]
Generators	[19230950:230013497:125000]	Generators of the group modulo torsion
j	24464768327/12691990927	j-invariant
L	6.9354153350321	L(r)(E,1)/r!
Ω	0.59111619729362	Real period
R	11.732744537851	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	97328bl1 54747i1 42581d1 66913i1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 6083a1

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	2	2	+	+	0	-2	-2	0	2	-8	10	-10	-4	-2	6	-10	-10	-4	12	0	+	-14	-2	-6

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Quadratic twists for elliptic curve 6083a1

-4	-3	-7	-11
97328bl1	54747i1	42581d1	66913i1

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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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