Cremona's table of elliptic curves

1584 = 2⁴ · 3² · 11

Field	Data	Notes
Atkin-Lehner	2- 3+ 11-	Signs for the Atkin-Lehner involutions
Class	1584j	Isogeny class
Conductor	1584	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	4982833152 = 224 · 33 · 11	Discriminant
Eigenvalues	2- 3+  0 -2 11-  2 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1035,-12358]	[a1,a2,a3,a4,a6]
Generators	[-17:18:1]	Generators of the group modulo torsion
j	1108717875/45056	j-invariant
L	2.7441828999857	L(r)(E,1)/r!
Ω	0.84382374251097	Real period
R	1.6260403457124	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	198c1 6336bi1 1584h3 39600ce1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1584j1

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
-	+	0	-2	-	2	-6	-2	0	-6	4	2	6	10	-12	-12	-12	-10	-8	-12	14	-2	12	0	2

---

Quadratic twists for elliptic curve 1584j1

-4	8	-3	5	-7	-11
198c1	6336bi1	1584h3	39600ce1	77616dq1	17424bc1

---

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