Cremona's table of elliptic curves

448 = 2⁶ · 7

Field	Data	Notes
Atkin-Lehner	2- 7+	Signs for the Atkin-Lehner involutions
Class	448d	Isogeny class
Conductor	448	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	32	Modular degree for the optimal curve
Δ	-28672 = -1 · 212 · 7	Discriminant
Eigenvalues	2-  2  0 7+  4  4 -2  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,7,-7]	[a1,a2,a3,a4,a6]
j	8000/7	j-invariant
L	2.0546257720226	L(r)(E,1)/r!
Ω	2.0546257720226	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	448g1 224a1 4032ba1 11200cr1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 448d1

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
-	2	0	+	4	4	-2	6	8	-2	-4	-10	-10	-4	4	2	-10	8	8	0	-6	-16	-2	18	-2

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Quadratic twists for elliptic curve 448d1

-4	8	-3	5	-7	-11	13	17
448g1	224a1	4032ba1	11200cr1	3136ba1	54208cx1	75712cu1	129472di1

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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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