Cremona's table of elliptic curves

32224 = 2⁵ · 19 · 53

Field	Data	Notes
Atkin-Lehner	2- 19- 53+	Signs for the Atkin-Lehner involutions
Class	32224b	Isogeny class
Conductor	32224	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	6016	Modular degree for the optimal curve
Δ	-9796096 = -1 · 29 · 192 · 53	Discriminant
Eigenvalues	2-  0 -3 -2 -5  2 -1 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-179,-934]	[a1,a2,a3,a4,a6]
Generators	[22:76:1]	Generators of the group modulo torsion
j	-1238833224/19133	j-invariant
L	2.5043525830955	L(r)(E,1)/r!
Ω	0.65201522142616	Real period
R	1.9204709497562	Regulator
r	1	Rank of the group of rational points
S	0.99999999999998	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	32224a1 64448d1	Quadratic twists by: -4 8

Hecke Eigenvalues for elliptic curve 32224b1

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	-3	-2	-5	2	-1	-	-1	0	-1	2	-8	9	-6	+	-9	2	8	-8	0	-3	0	15	5

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Quadratic twists for elliptic curve 32224b1

-4	8
32224a1	64448d1

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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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