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	240	Product of Tamagawa factors cp
Δ	2394017892421875000 = 23 · 32 · 510 · 237	Discriminant
Eigenvalues	2- 3- 5-  0 -2  0 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-415805,71440377]	[a1,a2,a3,a4,a6]
Generators	[964:23323:1]	Generators of the group modulo torsion
j	53706380371489/16171875000	j-invariant
L	9.1554289276071	L(r)(E,1)/r!
Ω	0.23950528578813	Real period
R	0.63710694995586	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	126960bq2 47610m2 79350c2 690i2	Quadratic twists by: -4 -3 5 -23

Hecke Eigenvalues for elliptic curve 15870bk2

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 15870bk2

-4	-3	5	-23
126960bq2	47610m2	79350c2	690i2

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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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