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	4719d	Isogeny class
Conductor	4719	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	151792661163 = 3 · 116 · 134	Discriminant
Eigenvalues	-1 3+  2  4 11- 13+ -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-2362,-40996]	[a1,a2,a3,a4,a6]
j	822656953/85683	j-invariant
L	1.3788648268565	L(r)(E,1)/r!
Ω	0.68943241342824	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	75504cn3 14157j4 117975by3 39a3	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 4719d3

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

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Quadratic twists for elliptic curve 4719d3

-4	-3	5	-11	13
75504cn3	14157j4	117975by3	39a3	61347k3

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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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