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	15870t	Isogeny class
Conductor	15870	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	11520	Modular degree for the optimal curve
Δ	-1300070400 = -1 · 215 · 3 · 52 · 232	Discriminant
Eigenvalues	2+ 3- 5- -3  1 -6  0 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-253,-2344]	[a1,a2,a3,a4,a6]
j	-3366353209/2457600	j-invariant
L	1.1605624818932	L(r)(E,1)/r!
Ω	0.58028124094659	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	126960ca1 47610by1 79350cm1 15870m1	Quadratic twists by: -4 -3 5 -23

Hecke Eigenvalues for elliptic curve 15870t1

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

---

Quadratic twists for elliptic curve 15870t1

-4	-3	5	-23
126960ca1	47610by1	79350cm1	15870m1

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations