Cremona's table of elliptic curves

4059 = 3² · 11 · 41

Field	Data	Notes
Atkin-Lehner	3- 11+ 41+	Signs for the Atkin-Lehner involutions
Class	4059a	Isogeny class
Conductor	4059	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2496	Modular degree for the optimal curve
Δ	4893217857 = 37 · 113 · 412	Discriminant
Eigenvalues	-1 3- -2  4 11+  0 -6  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-626,-4840]	[a1,a2,a3,a4,a6]
j	37159393753/6712233	j-invariant
L	0.96643399380107	L(r)(E,1)/r!
Ω	0.96643399380107	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	64944bo1 1353d1 101475be1 44649o1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 4059a1

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	+	0	-6	0	6	10	4	2	+	2	0	-12	-6	6	4	0	-14	-8	16	16	-6

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Quadratic twists for elliptic curve 4059a1

-4	-3	5	-11
64944bo1	1353d1	101475be1	44649o1

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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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