Cremona's table of elliptic curves

4199 = 13 · 17 · 19

Field	Data	Notes
Atkin-Lehner	13+ 17+ 19+	Signs for the Atkin-Lehner involutions
Class	4199a	Isogeny class
Conductor	4199	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	240	Modular degree for the optimal curve
Δ	-71383 = -1 · 13 · 172 · 19	Discriminant
Eigenvalues	1  2  0  2 -2 13+ 17+ 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,0,-13]	[a1,a2,a3,a4,a6]
Generators	[128144:666707:4096]	Generators of the group modulo torsion
j	-15625/71383	j-invariant
L	5.9953108330701	L(r)(E,1)/r!
Ω	1.5713612221297	Real period
R	7.6307226481566	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	67184o1 37791e1 104975i1 54587b1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 4199a1

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	0	2	-2	+	+	+	-8	4	-4	6	2	-4	-4	-6	-4	-2	4	0	-8	6	4	18	-10

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Quadratic twists for elliptic curve 4199a1

-4	-3	5	13	17	-19
67184o1	37791e1	104975i1	54587b1	71383a1	79781c1

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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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