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	32448c	Isogeny class
Conductor	32448	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	43008	Modular degree for the optimal curve
Δ	5204612994048 = 210 · 34 · 137	Discriminant
Eigenvalues	2+ 3+  2  0  0 13+  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-4957,79117]	[a1,a2,a3,a4,a6]
Generators	[-39:460:1]	Generators of the group modulo torsion
j	2725888/1053	j-invariant
L	5.3878174307319	L(r)(E,1)/r!
Ω	0.6972661247887	Real period
R	3.8635301782118	Regulator
r	1	Rank of the group of rational points
S	0.99999999999999	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	32448da1 4056f1 97344by1 2496c1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 32448c1

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	0	+	2	-4	0	-6	0	-2	-6	12	4	-6	-8	2	4	12	14	0	8	18	6

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Quadratic twists for elliptic curve 32448c1

-4	8	-3	13
32448da1	4056f1	97344by1	2496c1

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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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