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	8	Product of Tamagawa factors cp
deg	64	Modular degree for the optimal curve
Δ	1000000 = 26 · 56	Discriminant
Eigenvalues	2+  0 5+  0  0 -6 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-25,0]	[a1,a2,a3,a4,a6]
Generators	[-4:6:1]	Generators of the group modulo torsion
j	1728	j-invariant
L	2.2273703795441	L(r)(E,1)/r!
Ω	2.3452395729256	Real period
R	1.8994821725318	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	800a1 1600o2 7200bg1 32a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 800a1

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 800a1

-4	8	-3	5	-7	-11
800a1	1600o2	7200bg1	32a2	39200f1	96800bm1

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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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