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	32448cz	Isogeny class
Conductor	32448	Conductor
∏ cp	40	Product of Tamagawa factors cp
Δ	15176651490643968 = 212 · 310 · 137	Discriminant
Eigenvalues	2- 3-  0 -2  4 13+ -6  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-66473,-2917641]	[a1,a2,a3,a4,a6]
Generators	[-230:507:1]	Generators of the group modulo torsion
j	1643032000/767637	j-invariant
L	6.7729409815459	L(r)(E,1)/r!
Ω	0.31107609466569	Real period
R	2.1772618011117	Regulator
r	1	Rank of the group of rational points
S	0.99999999999997	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	32448bx2 16224n1 97344eq2 2496y2	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 32448cz2

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

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Quadratic twists for elliptic curve 32448cz2

-4	8	-3	13
32448bx2	16224n1	97344eq2	2496y2

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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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