Cremona's table of elliptic curves

18800 = 2⁴ · 5² · 47

Field	Data	Notes
Atkin-Lehner	2- 5- 47+	Signs for the Atkin-Lehner involutions
Class	18800bk	Isogeny class
Conductor	18800	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	13440	Modular degree for the optimal curve
Δ	23500000000 = 28 · 59 · 47	Discriminant
Eigenvalues	2- -1 5- -3  3 -5  4 -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1708,-25588]	[a1,a2,a3,a4,a6]
Generators	[-214:125:8]	Generators of the group modulo torsion
j	1102736/47	j-invariant
L	3.1864360475726	L(r)(E,1)/r!
Ω	0.74455751604439	Real period
R	2.1398186029342	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	4700l1 75200df1 18800bo1	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 18800bk1

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
-	-1	-	-3	3	-5	4	-5	2	8	-3	-2	0	-6	+	0	0	13	-8	-10	11	14	-5	-10	16

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Quadratic twists for elliptic curve 18800bk1

-4	8	5
4700l1	75200df1	18800bo1

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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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