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	4719f	Isogeny class
Conductor	4719	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	-61347 = -1 · 3 · 112 · 132	Discriminant
Eigenvalues	0 3+  2 -3 11- 13- -2 -7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-7,-12]	[a1,a2,a3,a4,a6]
Generators	[8:19:1]	Generators of the group modulo torsion
j	-360448/507	j-invariant
L	2.6623140501847	L(r)(E,1)/r!
Ω	1.3799898179993	Real period
R	0.96461365709372	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	75504cz1 14157r1 117975bi1 4719a1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 4719f1

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	-3	-	-	-2	-7	8	6	5	-3	-4	4	6	-4	6	-11	-3	4	-3	5	6	-2	-13

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Quadratic twists for elliptic curve 4719f1

-4	-3	5	-11	13
75504cz1	14157r1	117975bi1	4719a1	61347d1

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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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