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	15870m	Isogeny class
Conductor	15870	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	264960	Modular degree for the optimal curve
Δ	-192457077426585600 = -1 · 215 · 3 · 52 · 238	Discriminant
Eigenvalues	2+ 3- 5+  3 -1 -6  0  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-133584,28249246]	[a1,a2,a3,a4,a6]
Generators	[6456:82111:27]	Generators of the group modulo torsion
j	-3366353209/2457600	j-invariant
L	4.3372373785772	L(r)(E,1)/r!
Ω	0.2931577764581	Real period
R	7.3974455512988	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	126960bj1 47610ck1 79350cp1 15870t1	Quadratic twists by: -4 -3 5 -23

Hecke Eigenvalues for elliptic curve 15870m1

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	-1	-6	0	4	-	9	-11	-6	-2	-2	10	-5	3	-2	10	-10	-1	15	-1	-14	13

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Quadratic twists for elliptic curve 15870m1

-4	-3	5	-23
126960bj1	47610ck1	79350cp1	15870t1

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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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