Cremona's table of elliptic curves

15162 = 2 · 3 · 7 · 19²

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 19+	Signs for the Atkin-Lehner involutions
Class	15162ba	Isogeny class
Conductor	15162	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	60800	Modular degree for the optimal curve
Δ	189740366294052 = 22 · 3 · 72 · 199	Discriminant
Eigenvalues	2- 3-  0 7+ -6  2  2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-16433,465765]	[a1,a2,a3,a4,a6]
Generators	[1062:484037:729]	Generators of the group modulo torsion
j	1520875/588	j-invariant
L	8.2404409044152	L(r)(E,1)/r!
Ω	0.51667830665216	Real period
R	7.9744405738741	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	121296by1 45486e1 106134bt1 15162b1	Quadratic twists by: -4 -3 -7 -19

Hecke Eigenvalues for elliptic curve 15162ba1

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

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Quadratic twists for elliptic curve 15162ba1

-4	-3	-7	-19
121296by1	45486e1	106134bt1	15162b1

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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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