Cremona's table of elliptic curves

15990 = 2 · 3 · 5 · 13 · 41

Field	Data	Notes
Atkin-Lehner	2+ 3- 5- 13+ 41+	Signs for the Atkin-Lehner involutions
Class	15990k	Isogeny class
Conductor	15990	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	10080	Modular degree for the optimal curve
Δ	-119733120 = -1 · 27 · 33 · 5 · 132 · 41	Discriminant
Eigenvalues	2+ 3- 5- -5  2 13+  6 -1	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-68,-574]	[a1,a2,a3,a4,a6]
Generators	[12:13:1]	Generators of the group modulo torsion
j	-34043726521/119733120	j-invariant
L	4.0630648674852	L(r)(E,1)/r!
Ω	0.76438554966391	Real period
R	0.88591088386215	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	127920bk1 47970be1 79950bj1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 15990k1

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
+	-	-	-5	2	+	6	-1	3	-4	-5	-3	+	-1	-6	11	-9	-14	-8	16	8	-4	16	-9	-14

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Quadratic twists for elliptic curve 15990k1

-4	-3	5
127920bk1	47970be1	79950bj1

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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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