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	8	Product of Tamagawa factors cp
deg	1600	Modular degree for the optimal curve
Δ	9400625 = 54 · 132 · 89	Discriminant
Eigenvalues	-1  0 5- -4 -4 13+  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-322,2296]	[a1,a2,a3,a4,a6]
Generators	[-14:69:1]	Generators of the group modulo torsion
j	3681512411121/9400625	j-invariant
L	1.9276199616524	L(r)(E,1)/r!
Ω	2.3105426331341	Real period
R	1.6685430807548	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	92560n1 52065e1 28925e1 75205a1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 5785b1

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 5785b1

-4	-3	5	13
92560n1	52065e1	28925e1	75205a1

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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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