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	8670t	Isogeny class
Conductor	8670	Conductor
∏ cp	28	Product of Tamagawa factors cp
deg	376992	Modular degree for the optimal curve
Δ	-5.0615685259298E+20	Discriminant
Eigenvalues	2- 3+ 5-  3 -2  1 17- -5	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,661515,1062713115]	[a1,a2,a3,a4,a6]
j	4589352212399/72559411200	j-invariant
L	3.4396359820172	L(r)(E,1)/r!
Ω	0.1228441422149	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	69360dy1 26010p1 43350bm1 8670w1	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 8670t1

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	-2	1	-	-5	0	4	-1	3	6	-1	0	-10	14	1	13	12	6	8	6	-12	7

---

Quadratic twists for elliptic curve 8670t1

-4	-3	5	17
69360dy1	26010p1	43350bm1	8670w1

---

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