Cremona's table of elliptic curves

6448 = 2⁴ · 13 · 31

Field	Data	Notes
Atkin-Lehner	2- 13- 31+	Signs for the Atkin-Lehner involutions
Class	6448j	Isogeny class
Conductor	6448	Conductor
∏ cp	36	Product of Tamagawa factors cp
Δ	-333936194271739904 = -1 · 215 · 139 · 312	Discriminant
Eigenvalues	2- -1  3  1  0 13-  3 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-36697744,85579407296]	[a1,a2,a3,a4,a6]
Generators	[3490:806:1]	Generators of the group modulo torsion
j	-1334387227199873180280337/81527391179624	j-invariant
L	4.1627073197994	L(r)(E,1)/r!
Ω	0.22959924929695	Real period
R	0.5036199344614	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	806e3 25792v3 58032bl3 83824ba3	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 6448j3

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	3	1	0	-	3	-2	-6	-6	+	-7	-6	1	-3	6	0	-10	4	3	2	-8	0	0	-10

---

Quadratic twists for elliptic curve 6448j3

-4	8	-3	13
806e3	25792v3	58032bl3	83824ba3

---

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