Cremona's table of elliptic curves

5785 = 5 · 13 · 89

Field	Data	Notes
Atkin-Lehner	5+ 13+ 89+	Signs for the Atkin-Lehner involutions
Class	5785a	Isogeny class
Conductor	5785	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1872	Modular degree for the optimal curve
Δ	18078125 = 56 · 13 · 89	Discriminant
Eigenvalues	2 -2 5+ -1  2 13+  1  1	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-66,15]	[a1,a2,a3,a4,a6]
Generators	[-38:121:8]	Generators of the group modulo torsion
j	32278933504/18078125	j-invariant
L	4.9546813397466	L(r)(E,1)/r!
Ω	1.8857472930685	Real period
R	1.3137182691336	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	92560g1 52065n1 28925d1 75205d1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 5785a1

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
2	-2	+	-1	2	+	1	1	8	4	8	-6	-3	-12	2	13	-7	-10	-14	6	-16	-11	1	+	-8

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Quadratic twists for elliptic curve 5785a1

-4	-3	5	13
92560g1	52065n1	28925d1	75205d1

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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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