Cremona's table of elliptic curves

2888 = 2³ · 19²

Field	Data	Notes
Atkin-Lehner	2+ 19+	Signs for the Atkin-Lehner involutions
Class	2888b	Isogeny class
Conductor	2888	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	1008	Modular degree for the optimal curve
Δ	-266897408 = -1 · 211 · 194	Discriminant
Eigenvalues	2+  1 -4  0  3  2  2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-120,-976]	[a1,a2,a3,a4,a6]
Generators	[91:866:1]	Generators of the group modulo torsion
j	-722	j-invariant
L	3.1487989120413	L(r)(E,1)/r!
Ω	0.68599872349612	Real period
R	4.590094418826	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	5776b1 23104e1 25992ba1 72200v1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2888b1

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	0	3	2	2	+	6	-4	-10	2	9	-4	-12	-2	-1	-8	9	-6	-9	-4	-5	-18	1

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Quadratic twists for elliptic curve 2888b1

-4	8	-3	5	-19
5776b1	23104e1	25992ba1	72200v1	2888e1

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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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