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	5785b	Isogeny class
Conductor	5785	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-363000170845 = -1 · 5 · 138 · 89	Discriminant
Eigenvalues	-1  0 5- -4 -4 13+  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,1778,2226]	[a1,a2,a3,a4,a6]
Generators	[820:10073:64]	Generators of the group modulo torsion
j	621939235923279/363000170845	j-invariant
L	1.9276199616524	L(r)(E,1)/r!
Ω	0.57763565828353	Real period
R	6.6741723230192	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	92560n3 52065e3 28925e3 75205a3	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 5785b4

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	0	-	-4	-4	+	2	4	-4	6	0	10	10	0	8	6	-12	6	4	-16	-14	-8	0	-	18

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Quadratic twists for elliptic curve 5785b4

-4	-3	5	13
92560n3	52065e3	28925e3	75205a3

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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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