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	15870bm	Isogeny class
Conductor	15870	Conductor
∏ cp	1560	Product of Tamagawa factors cp
deg	599040	Modular degree for the optimal curve
Δ	-1.07954798976E+19	Discriminant
Eigenvalues	2- 3- 5- -3 -5  0  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1284745,582256025]	[a1,a2,a3,a4,a6]
Generators	[-70:-25885:1]	Generators of the group modulo torsion
j	-443321577260160665089/20407334400000000	j-invariant
L	8.3797107646561	L(r)(E,1)/r!
Ω	0.22552413007331	Real period
R	0.023818335815227	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	126960cb1 47610s1 79350i1 15870bi1	Quadratic twists by: -4 -3 5 -23

Hecke Eigenvalues for elliptic curve 15870bm1

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	-5	0	6	-4	-	-3	7	0	4	-10	4	11	-15	-4	-4	-10	5	-9	-11	-10	-7

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Quadratic twists for elliptic curve 15870bm1

-4	-3	5	-23
126960cb1	47610s1	79350i1	15870bi1

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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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