Cremona's table of elliptic curves

2550 = 2 · 3 · 5² · 17

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 17+	Signs for the Atkin-Lehner involutions
Class	2550x	Isogeny class
Conductor	2550	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	1280	Modular degree for the optimal curve
Δ	-27744000 = -1 · 28 · 3 · 53 · 172	Discriminant
Eigenvalues	2- 3+ 5- -4 -2  4 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-453,3531]	[a1,a2,a3,a4,a6]
Generators	[9:12:1]	Generators of the group modulo torsion
j	-82256120549/221952	j-invariant
L	3.7245903260591	L(r)(E,1)/r!
Ω	2.111901430174	Real period
R	0.22045242458074	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	20400dt1 81600eq1 7650bh1 2550p1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2550x1

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

---

Quadratic twists for elliptic curve 2550x1

-4	8	-3	5	-7	17
20400dt1	81600eq1	7650bh1	2550p1	124950jb1	43350dr1

---

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