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	15870bd	Isogeny class
Conductor	15870	Conductor
∏ cp	14	Product of Tamagawa factors cp
deg	247296	Modular degree for the optimal curve
Δ	-397694507651030400 = -1 · 27 · 3 · 52 · 2310	Discriminant
Eigenvalues	2- 3+ 5- -3 -3  0 -2  6	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-5830,-30344125]	[a1,a2,a3,a4,a6]
j	-529/9600	j-invariant
L	1.9134244928262	L(r)(E,1)/r!
Ω	0.13667317805902	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	126960de1 47610r1 79350bi1 15870x1	Quadratic twists by: -4 -3 5 -23

Hecke Eigenvalues for elliptic curve 15870bd1

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
-	+	-	-3	-3	0	-2	6	-	-3	-7	-10	0	8	-10	9	-1	12	4	-2	-5	5	17	0	-9

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Quadratic twists for elliptic curve 15870bd1

-4	-3	5	-23
126960de1	47610r1	79350bi1	15870x1

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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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