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
Δ	53017193645 = 5 · 132 · 894	Discriminant
Eigenvalues	-1  0 5- -4 -4 13+  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-4672,-121234]	[a1,a2,a3,a4,a6]
Generators	[515:11312:1]	Generators of the group modulo torsion
j	11275740292429521/53017193645	j-invariant
L	1.9276199616524	L(r)(E,1)/r!
Ω	0.57763565828353	Real period
R	1.6685430807548	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	92560n4 52065e4 28925e4 75205a4	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 5785b3

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 5785b3

-4	-3	5	13
92560n4	52065e4	28925e4	75205a4

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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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