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	15870j	Isogeny class
Conductor	15870	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	25536190852500 = 22 · 3 · 54 · 237	Discriminant
Eigenvalues	2+ 3- 5+  0 -4 -2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-778964,264555662]	[a1,a2,a3,a4,a6]
Generators	[-784:20229:1]	Generators of the group modulo torsion
j	353108405631241/172500	j-invariant
L	3.6593256129537	L(r)(E,1)/r!
Ω	0.54835016124927	Real period
R	1.6683343379607	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	126960z4 47610cd4 79350cd4 690f3	Quadratic twists by: -4 -3 5 -23

Hecke Eigenvalues for elliptic curve 15870j3

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	-4	-2	-2	0	-	6	0	-2	2	12	8	2	0	-6	-12	12	-6	-4	4	6	10

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Quadratic twists for elliptic curve 15870j3

-4	-3	5	-23
126960z4	47610cd4	79350cd4	690f3

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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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