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	1584f	Isogeny class
Conductor	1584	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-1625868288 = -1 · 211 · 38 · 112	Discriminant
Eigenvalues	2+ 3-  0 -2 11-  0  2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,285,578]	[a1,a2,a3,a4,a6]
Generators	[7:54:1]	Generators of the group modulo torsion
j	1714750/1089	j-invariant
L	2.740340604523	L(r)(E,1)/r!
Ω	0.93261527236037	Real period
R	0.73458495848653	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	792b2 6336bv2 528a2 39600ba2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1584f2

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

---

Quadratic twists for elliptic curve 1584f2

-4	8	-3	5	-7	-11
792b2	6336bv2	528a2	39600ba2	77616cb2	17424q2

---

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