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	6448d	Isogeny class
Conductor	6448	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	5760	Modular degree for the optimal curve
Δ	-4323977216 = -1 · 211 · 133 · 312	Discriminant
Eigenvalues	2+ -3 -3 -3 -2 13-  3 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-139,3226]	[a1,a2,a3,a4,a6]
Generators	[-2100679:-459628:117649] [-6:62:1]	Generators of the group modulo torsion
j	-145023426/2111317	j-invariant
L	2.876834371375	L(r)(E,1)/r!
Ω	1.1696574628563	Real period
R	0.10248136964352	Regulator
r	2	Rank of the group of rational points
S	1.0000000000001	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	3224d1 25792z1 58032m1 83824i1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 6448d1

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	-2	-	3	-4	2	-6	+	-1	-2	-5	-3	-10	-6	0	-12	-5	2	-6	-6	-4	-8

---

Quadratic twists for elliptic curve 6448d1

-4	8	-3	13
3224d1	25792z1	58032m1	83824i1

---

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