Cremona's table of elliptic curves

4719 = 3 · 11² · 13

Field	Data	Notes
Atkin-Lehner	3- 11- 13+	Signs for the Atkin-Lehner involutions
Class	4719j	Isogeny class
Conductor	4719	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	192533165626703187 = 3 · 1114 · 132	Discriminant
Eigenvalues	1 3- -2  0 11- 13+  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-364092,81851779]	[a1,a2,a3,a4,a6]
Generators	[-320103:9297244:729]	Generators of the group modulo torsion
j	3013001140430737/108679952667	j-invariant
L	4.7413140437719	L(r)(E,1)/r!
Ω	0.31629225643666	Real period
R	7.4951472052896	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	75504bj6 14157l5 117975q6 429b5	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 4719j5

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

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Quadratic twists for elliptic curve 4719j5

-4	-3	5	-11	13
75504bj6	14157l5	117975q6	429b5	61347z6

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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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