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	4059b	Isogeny class
Conductor	4059	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1600	Modular degree for the optimal curve
Δ	3275625177 = 311 · 11 · 412	Discriminant
Eigenvalues	1 3- -2  0 11+  4  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-378,751]	[a1,a2,a3,a4,a6]
Generators	[50:299:1]	Generators of the group modulo torsion
j	8205738913/4493313	j-invariant
L	3.8827138815824	L(r)(E,1)/r!
Ω	1.2308399017947	Real period
R	1.5772619476835	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	64944bt1 1353b1 101475bl1 44649l1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 4059b1

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

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Quadratic twists for elliptic curve 4059b1

-4	-3	5	-11
64944bt1	1353b1	101475bl1	44649l1

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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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