Cremona's table of elliptic curves

8670 = 2 · 3 · 5 · 17²

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 17-	Signs for the Atkin-Lehner involutions
Class	8670d	Isogeny class
Conductor	8670	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	514080	Modular degree for the optimal curve
Δ	-9.5349884521669E+21	Discriminant
Eigenvalues	2+ 3+ 5+ -1  2  1 17- -1	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-1227533,-4727641827]	[a1,a2,a3,a4,a6]
j	-29324621982169/1366875000000	j-invariant
L	0.90686264967735	L(r)(E,1)/r!
Ω	0.056678915604834	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	69360dg1 26010ca1 43350df1 8670j1	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 8670d1

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
+	+	+	-1	2	1	-	-1	-4	8	7	3	2	-9	8	-2	-6	5	-11	8	-2	0	2	4	3

---

Quadratic twists for elliptic curve 8670d1

-4	-3	5	17
69360dg1	26010ca1	43350df1	8670j1

---

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