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	32448a	Isogeny class
Conductor	32448	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	9252645322752 = 214 · 32 · 137	Discriminant
Eigenvalues	2+ 3+  0  0  6 13+  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-46193,-3803151]	[a1,a2,a3,a4,a6]
Generators	[6717:5408:27]	Generators of the group modulo torsion
j	137842000/117	j-invariant
L	5.4949012703687	L(r)(E,1)/r!
Ω	0.3256693285077	Real period
R	4.2181599473517	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	32448cu2 4056p2 97344x2 2496d2	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 32448a2

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	0	6	+	2	0	4	6	4	-2	0	-4	-10	10	-6	6	-12	-2	-6	-16	6	-4	-14

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Quadratic twists for elliptic curve 32448a2

-4	8	-3	13
32448cu2	4056p2	97344x2	2496d2

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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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