Cremona's table of elliptic curves

800 = 2⁵ · 5²

Field	Data	Notes
Atkin-Lehner	2- 5-	Signs for the Atkin-Lehner involutions
Class	800h	Isogeny class
Conductor	800	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-512000 = -1 · 212 · 53	Discriminant
Eigenvalues	2-  0 5-  0  0 -4 -8  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,20,0]	[a1,a2,a3,a4,a6]
Generators	[4:12:1]	Generators of the group modulo torsion
j	1728	j-invariant
L	2.2287681477468	L(r)(E,1)/r!
Ω	1.753475568523	Real period
R	1.2710574288891	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	800h2 1600t1 7200q2 800d2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 800h2

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	-4	-8	0	0	10	0	-12	-10	0	0	4	0	10	0	0	-16	0	0	-10	8

---

Quadratic twists for elliptic curve 800h2

-4	8	-3	5	-7	-11
800h2	1600t1	7200q2	800d2	39200cm2	96800bc2

---

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