Cremona's table of elliptic curves

5390 = 2 · 5 · 7² · 11

Field	Data	Notes
Atkin-Lehner	2+ 5+ 7- 11-	Signs for the Atkin-Lehner involutions
Class	5390j	Isogeny class
Conductor	5390	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	12288	Modular degree for the optimal curve
Δ	-15943792480000 = -1 · 28 · 54 · 77 · 112	Discriminant
Eigenvalues	2+  2 5+ 7- 11-  0  0  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,1592,-189888]	[a1,a2,a3,a4,a6]
Generators	[741:19842:1]	Generators of the group modulo torsion
j	3789119879/135520000	j-invariant
L	3.7956723496727	L(r)(E,1)/r!
Ω	0.33547501201101	Real period
R	1.4142902652121	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	43120bj1 48510ds1 26950cw1 770d1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5390j1

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
+	2	+	-	-	0	0	0	-4	2	2	-6	-8	-12	6	-6	10	4	-8	-4	4	-16	0	6	-14

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Quadratic twists for elliptic curve 5390j1

-4	-3	5	-7	-11
43120bj1	48510ds1	26950cw1	770d1	59290df1

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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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