Cremona's table of elliptic curves

585 = 3² · 5 · 13

Field	Data	Notes
Atkin-Lehner	3- 5- 13+	Signs for the Atkin-Lehner involutions
Class	585i	Isogeny class
Conductor	585	Conductor
∏ cp	28	Product of Tamagawa factors cp
deg	672	Modular degree for the optimal curve
Δ	-19990546875 = -1 · 39 · 57 · 13	Discriminant
Eigenvalues	-2 3- 5- -1 -5 13+  7 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-597,8820]	[a1,a2,a3,a4,a6]
Generators	[8:67:1]	Generators of the group modulo torsion
j	-32278933504/27421875	j-invariant
L	1.1749876121653	L(r)(E,1)/r!
Ω	1.113951504727	Real period
R	0.037671158137087	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	9360bt1 37440bp1 195c1 2925l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 585i1

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	-	-	-1	-5	+	7	-6	-3	-2	2	7	-9	-8	-10	-5	0	5	-4	-9	-6	-3	4	-11	-11

---

Quadratic twists for elliptic curve 585i1

-4	8	-3	5	-7	-11	13
9360bt1	37440bp1	195c1	2925l1	28665bh1	70785bg1	7605k1

---

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