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	2	Product of Tamagawa factors cp
Δ	-340805654937600 = -1 · 233 · 3 · 52 · 232	Discriminant
Eigenvalues	2+ 3- 5+  1  3 -4  6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,7751,849116]	[a1,a2,a3,a4,a6]
Generators	[-306:5789:8]	Generators of the group modulo torsion
j	97369242756359/644245094400	j-invariant
L	4.3720916408325	L(r)(E,1)/r!
Ω	0.39212194821542	Real period
R	5.5749131880149	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	126960bd2 47610cf2 79350cj2 15870r2	Quadratic twists by: -4 -3 5 -23

Hecke Eigenvalues for elliptic curve 15870k2

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 15870k2

-4	-3	5	-23
126960bd2	47610cf2	79350cj2	15870r2

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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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