Cremona's table of elliptic curves

2059 = 29 · 71

Field	Data	Notes
Atkin-Lehner	29+ 71-	Signs for the Atkin-Lehner involutions
Class	2059a	Isogeny class
Conductor	2059	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	280	Modular degree for the optimal curve
Δ	-2059 = -1 · 29 · 71	Discriminant
Eigenvalues	-2 -2 -1  0 -4 -6 -6  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-36,72]	[a1,a2,a3,a4,a6]
Generators	[5:6:1] [0:8:1]	Generators of the group modulo torsion
j	-5304438784/2059	j-invariant
L	1.4736603975424	L(r)(E,1)/r!
Ω	4.5685888755038	Real period
R	0.3225635831328	Regulator
r	2	Rank of the group of rational points
S	0.99999999999952	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	32944c1 18531e1 51475a1 100891e1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2059a1

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
-2	-2	-1	0	-4	-6	-6	2	4	+	-7	-2	9	-8	-11	-12	-10	-5	-2	-	-2	-10	1	-2	-17

---

Quadratic twists for elliptic curve 2059a1

-4	-3	5	-7	29
32944c1	18531e1	51475a1	100891e1	59711a1

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations