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	4719g	Isogeny class
Conductor	4719	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	342144	Modular degree for the optimal curve
Δ	-86278949503230627 = -1 · 39 · 1110 · 132	Discriminant
Eigenvalues	0 3+  2  5 11- 13- -2  1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-47690617,126780363258]	[a1,a2,a3,a4,a6]
Generators	[9308:699445:1]	Generators of the group modulo torsion
j	-462482914449031168/3326427	j-invariant
L	3.5280886109695	L(r)(E,1)/r!
Ω	0.23460315943554	Real period
R	7.5192691766346	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	75504db1 14157s1 117975bk1 4719b1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 4719g1

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
0	+	2	5	-	-	-2	1	-8	-10	-3	-11	-4	4	-10	-4	-10	5	5	-12	-11	-11	6	14	11

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Quadratic twists for elliptic curve 4719g1

-4	-3	5	-11	13
75504db1	14157s1	117975bk1	4719b1	61347h1

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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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