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	2800d	Isogeny class
Conductor	2800	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	480	Modular degree for the optimal curve
Δ	-6722800 = -1 · 24 · 52 · 75	Discriminant
Eigenvalues	2+  2 5+ 7+ -1 -4  0 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-28,147]	[a1,a2,a3,a4,a6]
Generators	[3:9:1]	Generators of the group modulo torsion
j	-6288640/16807	j-invariant
L	4.2293432906205	L(r)(E,1)/r!
Ω	2.0911532397931	Real period
R	2.0224932396819	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	1400k1 11200cd1 25200x1 2800n1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2800d1

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
+	2	+	+	-1	-4	0	-6	3	-3	0	-9	2	9	-6	-6	-8	-10	-1	7	2	9	12	-4	-16

---

Quadratic twists for elliptic curve 2800d1

-4	8	-3	5	-7
1400k1	11200cd1	25200x1	2800n1	19600x1

---

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