Cremona's table of elliptic curves

1888 = 2⁵ · 59

Field	Data	Notes
Atkin-Lehner	2- 59-	Signs for the Atkin-Lehner involutions
Class	1888d	Isogeny class
Conductor	1888	Conductor
∏ cp	6	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]
Generators	[29:118:1]	Generators of the group modulo torsion
j	-238789577664/205379	j-invariant
L	1.8295108955652	L(r)(E,1)/r!
Ω	2.2254811594465	Real period
R	0.13701238552388	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	1888b1 3776q1 16992a1 47200m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1888d1

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 1888d1

-4	8	-3	5	-7	-59
1888b1	3776q1	16992a1	47200m1	92512i1	111392f1

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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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