Cremona's table of elliptic curves

5985 = 3² · 5 · 7 · 19

Field	Data	Notes
Atkin-Lehner	3- 5+ 7+ 19-	Signs for the Atkin-Lehner involutions
Class	5985i	Isogeny class
Conductor	5985	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	3325140315 = 36 · 5 · 7 · 194	Discriminant
Eigenvalues	-1 3- 5+ 7+  4 -2 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-1748,-27548]	[a1,a2,a3,a4,a6]
Generators	[-23:20:1]	Generators of the group modulo torsion
j	809818183161/4561235	j-invariant
L	2.2788987964762	L(r)(E,1)/r!
Ω	0.73863673605717	Real period
R	1.542638407508	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	95760dn4 665b3 29925be4 41895bl4	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5985i3

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	-	+	+	4	-2	-2	-	8	-6	-8	-6	-6	4	-8	6	12	-2	4	12	-6	12	4	10	2

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Quadratic twists for elliptic curve 5985i3

-4	-3	5	-7	-19
95760dn4	665b3	29925be4	41895bl4	113715m4

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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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