Cremona's table of elliptic curves

32800 = 2⁵ · 5² · 41

Field	Data	Notes
Atkin-Lehner	2- 5+ 41-	Signs for the Atkin-Lehner involutions
Class	32800o	Isogeny class
Conductor	32800	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	9216	Modular degree for the optimal curve
Δ	1025000000 = 26 · 58 · 41	Discriminant
Eigenvalues	2-  0 5+ -2  2 -2  0 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-425,3000]	[a1,a2,a3,a4,a6]
Generators	[20:50:1]	Generators of the group modulo torsion
j	8489664/1025	j-invariant
L	4.4006373533267	L(r)(E,1)/r!
Ω	1.5052656102364	Real period
R	1.4617477883639	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	32800n1 65600bt1 6560e1	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 32800o1

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	+	-2	2	-2	0	-6	4	-4	0	6	-	-4	6	10	4	2	16	-8	-2	-4	-12	6	12

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Quadratic twists for elliptic curve 32800o1

-4	8	5
32800n1	65600bt1	6560e1

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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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