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	1584p	Isogeny class
Conductor	1584	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	240	Modular degree for the optimal curve
Δ	-32845824 = -1 · 212 · 36 · 11	Discriminant
Eigenvalues	2- 3- -1  2 11-  4  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-48,304]	[a1,a2,a3,a4,a6]
j	-4096/11	j-invariant
L	1.8319458337094	L(r)(E,1)/r!
Ω	1.8319458337094	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	99d1 6336bx1 176b1 39600dy1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1584p1

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
-	-	-1	2	-	4	2	0	-1	0	-7	3	8	6	8	6	5	12	7	-3	4	10	-6	-15	-7

---

Quadratic twists for elliptic curve 1584p1

-4	8	-3	5	-7	-11
99d1	6336bx1	176b1	39600dy1	77616ga1	17424bv1

---

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