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	6448b	Isogeny class
Conductor	6448	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2688	Modular degree for the optimal curve
Δ	-4323977216 = -1 · 211 · 133 · 312	Discriminant
Eigenvalues	2+ -1  1  3 -4 13+  3  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1160,-15152]	[a1,a2,a3,a4,a6]
j	-84361067282/2111317	j-invariant
L	1.6335852416975	L(r)(E,1)/r!
Ω	0.40839631042438	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	3224a1 25792bh1 58032i1 83824a1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 6448b1

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	1	3	-4	+	3	2	6	-2	-	-5	-2	-7	7	2	0	6	0	9	14	12	4	-16	-10

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Quadratic twists for elliptic curve 6448b1

-4	8	-3	13
3224a1	25792bh1	58032i1	83824a1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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