Cremona's table of elliptic curves

1888 = 2⁵ · 59

Field	Data	Notes
Atkin-Lehner	2- 59+	Signs for the Atkin-Lehner involutions
Class	1888b	Isogeny class
Conductor	1888	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	-13144256 = -1 · 26 · 593	Discriminant
Eigenvalues	2-  3  1  3  0  0  2  3	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-517,-4528]	[a1,a2,a3,a4,a6]
j	-238789577664/205379	j-invariant
L	4.0046494948195	L(r)(E,1)/r!
Ω	0.50058118685244	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1888d1 3776z1 16992d1 47200f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1888b1

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	1	3	0	0	2	3	-6	-1	-6	-2	7	-6	0	-7	+	-10	12	0	0	-3	0	10	-12

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Quadratic twists for elliptic curve 1888b1

-4	8	-3	5	-7	-59
1888d1	3776z1	16992d1	47200f1	92512l1	111392e1

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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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