Cremona's table of elliptic curves

18675 = 3² · 5² · 83

Field	Data	Notes
Atkin-Lehner	3- 5- 83+	Signs for the Atkin-Lehner involutions
Class	18675o	Isogeny class
Conductor	18675	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	138880	Modular degree for the optimal curve
Δ	-21451740521484375 = -1 · 313 · 59 · 832	Discriminant
Eigenvalues	1 3- 5-  4 -2 -2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,20133,6955416]	[a1,a2,a3,a4,a6]
Generators	[48648:10705584:1]	Generators of the group modulo torsion
j	633839779/15066243	j-invariant
L	6.3826929539408	L(r)(E,1)/r!
Ω	0.28677020739654	Real period
R	5.5642922358345	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	6225j1 18675r1	Quadratic twists by: -3 5

Hecke Eigenvalues for elliptic curve 18675o1

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	-	-	4	-2	-2	-6	4	-8	6	4	4	2	6	-12	2	14	2	-10	0	2	8	+	-4	-14

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Quadratic twists for elliptic curve 18675o1

-3	5
6225j1	18675r1

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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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