Cremona's table of elliptic curves

19044 = 2² · 3² · 23²

Field	Data	Notes
Atkin-Lehner	2- 3- 23-	Signs for the Atkin-Lehner involutions
Class	19044m	Isogeny class
Conductor	19044	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	11520	Modular degree for the optimal curve
Δ	-296172288 = -1 · 28 · 37 · 232	Discriminant
Eigenvalues	2- 3- -4 -3  0  1 -4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-552,5060]	[a1,a2,a3,a4,a6]
Generators	[-20:90:1] [16:-18:1]	Generators of the group modulo torsion
j	-188416/3	j-invariant
L	5.6543530482848	L(r)(E,1)/r!
Ω	1.7320504636923	Real period
R	0.2720452418878	Regulator
r	2	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	76176cm1 6348c1 19044l1	Quadratic twists by: -4 -3 -23

Hecke Eigenvalues for elliptic curve 19044m1

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

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Quadratic twists for elliptic curve 19044m1

-4	-3	-23
76176cm1	6348c1	19044l1

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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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