Cremona's table of elliptic curves

3224 = 2³ · 13 · 31

Field	Data	Notes
Atkin-Lehner	2+ 13+ 31+	Signs for the Atkin-Lehner involutions
Class	3224a	Isogeny class
Conductor	3224	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1344	Modular degree for the optimal curve
Δ	-4323977216 = -1 · 211 · 133 · 312	Discriminant
Eigenvalues	2+  1  1 -3  4 13+  3 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1160,15152]	[a1,a2,a3,a4,a6]
Generators	[11:62:1]	Generators of the group modulo torsion
j	-84361067282/2111317	j-invariant
L	3.9243618203701	L(r)(E,1)/r!
Ω	1.3797681037793	Real period
R	1.4221091970531	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	6448b1 25792r1 29016j1 80600z1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3224a1

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
+	1	1	-3	4	+	3	-2	-6	-2	+	-5	-2	7	-7	2	0	6	0	-9	14	-12	-4	-16	-10

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Quadratic twists for elliptic curve 3224a1

-4	8	-3	5	13	-31
6448b1	25792r1	29016j1	80600z1	41912h1	99944b1

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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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