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	32448f	Isogeny class
Conductor	32448	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	129024	Modular degree for the optimal curve
Δ	238219473915072 = 26 · 33 · 1310	Discriminant
Eigenvalues	2+ 3+ -2  0 -4 13+ -6  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-15604,-101882]	[a1,a2,a3,a4,a6]
Generators	[-918:3245:8]	Generators of the group modulo torsion
j	1360251712/771147	j-invariant
L	2.9975299231015	L(r)(E,1)/r!
Ω	0.46097527425487	Real period
R	6.5025828726856	Regulator
r	1	Rank of the group of rational points
S	1.0000000000001	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	32448bi1 16224t2 97344bo1 2496b1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 32448f1

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

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Quadratic twists for elliptic curve 32448f1

-4	8	-3	13
32448bi1	16224t2	97344bo1	2496b1

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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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