Cremona's table of elliptic curves

6050 = 2 · 5² · 11²

Field	Data	Notes
Atkin-Lehner	2- 5+ 11-	Signs for the Atkin-Lehner involutions
Class	6050bc	Isogeny class
Conductor	6050	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	11520	Modular degree for the optimal curve
Δ	-12179481875000 = -1 · 23 · 57 · 117	Discriminant
Eigenvalues	2- -1 5+ -1 11-  2 -3  1	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-3088,-181719]	[a1,a2,a3,a4,a6]
Generators	[215:2917:1]	Generators of the group modulo torsion
j	-117649/440	j-invariant
L	4.7342428453133	L(r)(E,1)/r!
Ω	0.29311555949389	Real period
R	0.6729773025196	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	48400bt1 54450bv1 1210c1 550a1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 6050bc1

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	-	2	-3	1	-6	9	5	-5	6	8	-6	-9	6	-5	-8	-9	-10	-14	-6	-15	-8

---

Quadratic twists for elliptic curve 6050bc1

-4	-3	5	-11
48400bt1	54450bv1	1210c1	550a1

---

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