Cremona's table of elliptic curves

18490 = 2 · 5 · 43²

Field	Data	Notes
Atkin-Lehner	2- 5+ 43-	Signs for the Atkin-Lehner involutions
Class	18490k	Isogeny class
Conductor	18490	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	3360	Modular degree for the optimal curve
Δ	-36980 = -1 · 22 · 5 · 432	Discriminant
Eigenvalues	2- -3 5+  0 -6  0 -4  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-3,-9]	[a1,a2,a3,a4,a6]
Generators	[3:0:1]	Generators of the group modulo torsion
j	-1161/20	j-invariant
L	3.4782449676669	L(r)(E,1)/r!
Ω	1.5712948239734	Real period
R	1.1068085105987	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	92450k1 18490d1	Quadratic twists by: 5 -43

Hecke Eigenvalues for elliptic curve 18490k1

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
-	-3	+	0	-6	0	-4	4	0	-9	4	8	5	-	-3	6	2	2	11	-8	-8	0	11	-13	-8

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Quadratic twists for elliptic curve 18490k1

5	-43
92450k1	18490d1

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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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