Cremona's table of elliptic curves

1849 = 43²

Field	Data	Notes
Atkin-Lehner	43+	Signs for the Atkin-Lehner involutions
Class	1849b	Isogeny class
Conductor	1849	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	210	Modular degree for the optimal curve
Δ	3418801 = 434	Discriminant
Eigenvalues	1  1 -1  3  0 -5  3  1	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-39,-27]	[a1,a2,a3,a4,a6]
Generators	[-3:9:1]	Generators of the group modulo torsion
j	1849	j-invariant
L	3.9737443304679	L(r)(E,1)/r!
Ω	2.0421256903159	Real period
R	1.945886264157	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	29584i1 118336d1 16641f1 46225b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1849b1

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	1	-1	3	0	-5	3	1	-7	3	5	-9	-10	+	-8	-5	12	-13	-3	-1	11	-5	9	-1	-2

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Quadratic twists for elliptic curve 1849b1

-4	8	-3	5	-7	-43
29584i1	118336d1	16641f1	46225b1	90601b1	1849c1

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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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