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	15870bk	Isogeny class
Conductor	15870	Conductor
∏ cp	120	Product of Tamagawa factors cp
deg	126720	Modular degree for the optimal curve
Δ	-46986591168600000 = -1 · 26 · 3 · 55 · 238	Discriminant
Eigenvalues	2- 3- 5-  0 -2  0 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,70875,7490625]	[a1,a2,a3,a4,a6]
Generators	[320:7775:1]	Generators of the group modulo torsion
j	265971760991/317400000	j-invariant
L	9.1554289276071	L(r)(E,1)/r!
Ω	0.23950528578813	Real period
R	1.2742138999117	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	126960bq1 47610m1 79350c1 690i1	Quadratic twists by: -4 -3 5 -23

Hecke Eigenvalues for elliptic curve 15870bk1

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	-2	0	-6	-4	-	0	-8	6	-2	2	4	2	0	2	2	-10	-10	0	4	-4	-16

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Quadratic twists for elliptic curve 15870bk1

-4	-3	5	-23
126960bq1	47610m1	79350c1	690i1

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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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