Cremona's table of elliptic curves

32448 = 2⁶ · 3 · 13²

Field	Data	Notes
Atkin-Lehner	2- 3+ 13+	Signs for the Atkin-Lehner involutions
Class	32448cr	Isogeny class
Conductor	32448	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	64512	Modular degree for the optimal curve
Δ	578290332672 = 210 · 32 · 137	Discriminant
Eigenvalues	2- 3+ -4 -2  4 13+  2  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-3605,-73659]	[a1,a2,a3,a4,a6]
j	1048576/117	j-invariant
L	1.2411693991768	L(r)(E,1)/r!
Ω	0.62058469959066	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	32448br1 8112bi1 97344gc1 2496v1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 32448cr1

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
-	+	-4	-2	4	+	2	2	0	6	-10	10	-8	4	-4	10	8	14	-2	16	10	16	0	4	2

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Quadratic twists for elliptic curve 32448cr1

-4	8	-3	13
32448br1	8112bi1	97344gc1	2496v1

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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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