Cremona's table of elliptic curves

3560 = 2³ · 5 · 89

Field	Data	Notes
Atkin-Lehner	2- 5+ 89+	Signs for the Atkin-Lehner involutions
Class	3560f	Isogeny class
Conductor	3560	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	512	Modular degree for the optimal curve
Δ	569600 = 28 · 52 · 89	Discriminant
Eigenvalues	2- -2 5+ -2 -4 -4 -6  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-36,64]	[a1,a2,a3,a4,a6]
Generators	[-6:10:1] [-5:12:1]	Generators of the group modulo torsion
j	20720464/2225	j-invariant
L	3.033629567097	L(r)(E,1)/r!
Ω	2.8213212631043	Real period
R	0.53762568743411	Regulator
r	2	Rank of the group of rational points
S	0.99999999999972	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	7120c1 28480n1 32040e1 17800a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3560f1

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
-	-2	+	-2	-4	-4	-6	0	2	-10	-8	-4	-10	-6	12	-2	-4	-2	4	0	10	0	-6	+	-2

---

Quadratic twists for elliptic curve 3560f1

-4	8	-3	5
7120c1	28480n1	32040e1	17800a1

---

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