Cremona's table of elliptic curves

12584 = 2³ · 11² · 13

Field	Data	Notes
Atkin-Lehner	2- 11- 13-	Signs for the Atkin-Lehner involutions
Class	12584l	Isogeny class
Conductor	12584	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	49920	Modular degree for the optimal curve
Δ	-5707090847744 = -1 · 211 · 118 · 13	Discriminant
Eigenvalues	2-  3  3  3 11- 13-  5 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,3509,-82522]	[a1,a2,a3,a4,a6]
j	1317006/1573	j-invariant
L	7.3405569340041	L(r)(E,1)/r!
Ω	0.40780871855578	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	9	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	25168m1 100672bd1 113256z1 1144a1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 12584l1

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
-	3	3	3	-	-	5	-4	8	0	0	-5	0	-11	-9	-6	6	0	8	-15	4	14	8	-12	-16

---

Quadratic twists for elliptic curve 12584l1

-4	8	-3	-11
25168m1	100672bd1	113256z1	1144a1

---

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