Cremona's table of elliptic curves

15870 = 2 · 3 · 5 · 23²

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 23-	Signs for the Atkin-Lehner involutions
Class	15870k	Isogeny class
Conductor	15870	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	25344	Modular degree for the optimal curve
Δ	-457056000000 = -1 · 211 · 33 · 56 · 232	Discriminant
Eigenvalues	2+ 3- 5+  1  3 -4  6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-874,-34084]	[a1,a2,a3,a4,a6]
Generators	[48:163:1]	Generators of the group modulo torsion
j	-139343861641/864000000	j-invariant
L	4.3720916408325	L(r)(E,1)/r!
Ω	0.39212194821542	Real period
R	1.858304396005	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	126960bd1 47610cf1 79350cj1 15870r1	Quadratic twists by: -4 -3 5 -23

Hecke Eigenvalues for elliptic curve 15870k1

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	3	-4	6	-2	-	-9	5	-2	-12	4	-6	3	9	4	-8	6	11	1	-9	-12	-17

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Quadratic twists for elliptic curve 15870k1

-4	-3	5	-23
126960bd1	47610cf1	79350cj1	15870r1

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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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