Cremona's table of elliptic curves

48672 = 2⁵ · 3² · 13²

Field	Data	Notes
Atkin-Lehner	2+ 3- 13-	Signs for the Atkin-Lehner involutions
Class	48672z	Isogeny class
Conductor	48672	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	24192	Modular degree for the optimal curve
Δ	-820025856 = -1 · 29 · 36 · 133	Discriminant
Eigenvalues	2+ 3- -3  1  4 13- -5 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-819,9126]	[a1,a2,a3,a4,a6]
Generators	[13:-26:1]	Generators of the group modulo torsion
j	-74088	j-invariant
L	4.5871547238558	L(r)(E,1)/r!
Ω	1.5927866383035	Real period
R	0.71998888826967	Regulator
r	1	Rank of the group of rational points
S	1.0000000000009	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	48672cb1 97344di1 5408m1 48672ca1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 48672z1

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	1	4	-	-5	-6	-6	4	0	3	12	3	7	2	-2	-12	-4	-11	-6	6	10	6	0

---

Quadratic twists for elliptic curve 48672z1

-4	8	-3	13
48672cb1	97344di1	5408m1	48672ca1

---

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