Cremona's table of elliptic curves

127050 = 2 · 3 · 5² · 7 · 11²

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 7- 11+	Signs for the Atkin-Lehner involutions
Class	127050gt	Isogeny class
Conductor	127050	Conductor
∏ cp	480	Product of Tamagawa factors cp
deg	645120	Modular degree for the optimal curve
Δ	103081499136000 = 212 · 32 · 53 · 75 · 113	Discriminant
Eigenvalues	2- 3+ 5- 7- 11+ -6 -4 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-22778,1220231]	[a1,a2,a3,a4,a6]
Generators	[149:-1153:1] [-145:1297:1]	Generators of the group modulo torsion
j	7855676688439/619573248	j-invariant
L	15.625196926321	L(r)(E,1)/r!
Ω	0.58341876297896	Real period
R	0.22318441353796	Regulator
r	2	Rank of the group of rational points
S	0.99999999941257	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	127050dt1 127050bq1	Quadratic twists by: 5 -11

Hecke Eigenvalues for elliptic curve 127050gt1

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

---

Quadratic twists for elliptic curve 127050gt1

5	-11
127050dt1	127050bq1

---

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