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	5985p	Isogeny class
Conductor	5985	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	14378675176578825 = 37 · 52 · 712 · 19	Discriminant
Eigenvalues	1 3- 5- 7+  0 -6 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-90459,8762040]	[a1,a2,a3,a4,a6]
j	112293400033564849/19723834261425	j-invariant
L	1.5073369552191	L(r)(E,1)/r!
Ω	0.37683423880476	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	95760ez3 1995e3 29925bf3 41895x3	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5985p4

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	-6	-6	-	-4	2	0	-2	6	4	8	10	12	14	-8	8	2	-4	-12	6	6

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Quadratic twists for elliptic curve 5985p4

-4	-3	5	-7	-19
95760ez3	1995e3	29925bf3	41895x3	113715be3

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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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