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	4	Product of Tamagawa factors cp
deg	1280	Modular degree for the optimal curve
Δ	-69090879 = -1 · 3 · 116 · 13	Discriminant
Eigenvalues	-1 3+  2  4 11- 13+ -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,58,386]	[a1,a2,a3,a4,a6]
j	12167/39	j-invariant
L	1.3788648268565	L(r)(E,1)/r!
Ω	1.3788648268565	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	75504cn1 14157j1 117975by1 39a4	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 4719d1

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 4719d1

-4	-3	5	-11	13
75504cn1	14157j1	117975by1	39a4	61347k1

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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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