Cremona's table of elliptic curves

800 = 2⁵ · 5²

Field	Data	Notes
Atkin-Lehner	2+ 5+	Signs for the Atkin-Lehner involutions
Class	800a	Isogeny class
Conductor	800	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	8000000 = 29 · 56	Discriminant
Eigenvalues	2+  0 5+  0  0 -6 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-275,1750]	[a1,a2,a3,a4,a6]
Generators	[-15:50:1]	Generators of the group modulo torsion
j	287496	j-invariant
L	2.2273703795441	L(r)(E,1)/r!
Ω	2.3452395729256	Real period
R	0.9497410862659	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	800a2 1600o4 7200bg2 32a4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 800a3

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	-6	-2	0	0	-10	0	2	10	0	0	-14	0	-10	0	0	6	0	0	10	-18

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Quadratic twists for elliptic curve 800a3

-4	8	-3	5	-7	-11
800a2	1600o4	7200bg2	32a4	39200f3	96800bm4

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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