Cremona's table of elliptic curves

35739 = 3² · 11 · 19²

Field	Data	Notes
Atkin-Lehner	3- 11+ 19-	Signs for the Atkin-Lehner involutions
Class	35739p	Isogeny class
Conductor	35739	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	17280	Modular degree for the optimal curve
Δ	3152501451 = 38 · 113 · 192	Discriminant
Eigenvalues	1 3- -1 -3 11+ -6  0 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-495,-3146]	[a1,a2,a3,a4,a6]
Generators	[-10:32:1]	Generators of the group modulo torsion
j	51026761/11979	j-invariant
L	3.7892065493104	L(r)(E,1)/r!
Ω	1.0292318115022	Real period
R	1.8407935447405	Regulator
r	1	Rank of the group of rational points
S	1.0000000000002	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	11913e1 35739k1	Quadratic twists by: -3 -19

Hecke Eigenvalues for elliptic curve 35739p1

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	-	-1	-3	+	-6	0	-	2	-4	4	7	4	-4	-6	-9	12	10	-14	-12	10	15	17	10	-1

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Quadratic twists for elliptic curve 35739p1

-3	-19
11913e1	35739k1

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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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