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	32448cq	Isogeny class
Conductor	32448	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	645120	Modular degree for the optimal curve
Δ	641213525479707648 = 210 · 310 · 139	Discriminant
Eigenvalues	2- 3+  4  0  2 13+  2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-440301,-105501267]	[a1,a2,a3,a4,a6]
j	1909913257984/129730653	j-invariant
L	2.9780599389	L(r)(E,1)/r!
Ω	0.18612874618144	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	32448bp1 8112q1 97344ge1 2496x1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 32448cq1

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	0	2	+	2	-8	-4	6	-4	6	12	4	-6	2	14	-10	4	2	2	8	-14	0	10

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Quadratic twists for elliptic curve 32448cq1

-4	8	-3	13
32448bp1	8112q1	97344ge1	2496x1

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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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