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	32	Product of Tamagawa factors cp
Δ	322382025 = 36 · 52 · 72 · 192	Discriminant
Eigenvalues	-1 3- 5+ 7+  4 -2 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-173,172]	[a1,a2,a3,a4,a6]
Generators	[-8:35:1]	Generators of the group modulo torsion
j	781229961/442225	j-invariant
L	2.2788987964762	L(r)(E,1)/r!
Ω	1.4772734721143	Real period
R	0.77131920375399	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	95760dn2 665b2 29925be2 41895bl2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5985i2

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 5985i2

-4	-3	5	-7	-19
95760dn2	665b2	29925be2	41895bl2	113715m2

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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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