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	2550a	Isogeny class
Conductor	2550	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	-63750000 = -1 · 24 · 3 · 57 · 17	Discriminant
Eigenvalues	2+ 3+ 5+  0  4 -2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,100,0]	[a1,a2,a3,a4,a6]
Generators	[4:20:1]	Generators of the group modulo torsion
j	6967871/4080	j-invariant
L	2.108248731355	L(r)(E,1)/r!
Ω	1.1564244169153	Real period
R	1.8230752486001	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	20400cy1 81600co1 7650cb1 510f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2550a1

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

---

Quadratic twists for elliptic curve 2550a1

-4	8	-3	5	-7	17
20400cy1	81600co1	7650cb1	510f1	124950dd1	43350bb1

---

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