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	4	Product of Tamagawa factors cp
Δ	-524577373652649603 = -1 · 3 · 118 · 138	Discriminant
Eigenvalues	1 3- -2  0 11- 13+  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,162258,-24099209]	[a1,a2,a3,a4,a6]
Generators	[800431096085339950:-25801682399716050523:942633335125000]	Generators of the group modulo torsion
j	266679605718863/296110251723	j-invariant
L	4.7413140437719	L(r)(E,1)/r!
Ω	0.15814612821833	Real period
R	29.980588821158	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	75504bj5 14157l6 117975q5 429b6	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 4719j6

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 4719j6

-4	-3	5	-11	13
75504bj5	14157l6	117975q5	429b6	61347z5

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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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