Cremona's table of elliptic curves

8900 = 2² · 5² · 89

Field	Data	Notes
Atkin-Lehner	2- 5+ 89-	Signs for the Atkin-Lehner involutions
Class	8900a	Isogeny class
Conductor	8900	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	3456	Modular degree for the optimal curve
Δ	111250000 = 24 · 57 · 89	Discriminant
Eigenvalues	2-  0 5+  0  0 -2 -2  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-3700,86625]	[a1,a2,a3,a4,a6]
Generators	[10:225:1]	Generators of the group modulo torsion
j	22407266304/445	j-invariant
L	4.0420802336819	L(r)(E,1)/r!
Ω	1.7277871572815	Real period
R	1.5596366395198	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	35600v1 80100k1 1780a1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 8900a1

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	+	0	0	-2	-2	2	4	2	-2	10	-6	8	-6	14	-6	10	-2	-8	-2	-12	16	-	-10

---

Quadratic twists for elliptic curve 8900a1

-4	-3	5
35600v1	80100k1	1780a1

---

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