Cremona's table of elliptic curves

2800 = 2⁴ · 5² · 7

Field	Data	Notes
Atkin-Lehner	2- 5- 7+	Signs for the Atkin-Lehner involutions
Class	2800bb	Isogeny class
Conductor	2800	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2880	Modular degree for the optimal curve
Δ	-3500000000 = -1 · 28 · 59 · 7	Discriminant
Eigenvalues	2- -3 5- 7+ -3  1 -5  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1000,-12500]	[a1,a2,a3,a4,a6]
Generators	[50:250:1]	Generators of the group modulo torsion
j	-221184/7	j-invariant
L	1.893947487992	L(r)(E,1)/r!
Ω	0.42370240571946	Real period
R	1.1174986632281	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	700j1 11200da1 25200fa1 2800bf1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2800bb1

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
-	-3	-	+	-3	1	-5	8	-2	-1	2	10	-6	4	-11	6	10	0	10	0	-10	7	-12	8	3

---

Quadratic twists for elliptic curve 2800bb1

-4	8	-3	5	-7
700j1	11200da1	25200fa1	2800bf1	19600ec1

---

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