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	3224c	Isogeny class
Conductor	3224	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	864	Modular degree for the optimal curve
Δ	-80554864 = -1 · 24 · 132 · 313	Discriminant
Eigenvalues	2- -2 -1 -1 -2 13+  0  7	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-536,-4979]	[a1,a2,a3,a4,a6]
Generators	[58:403:1]	Generators of the group modulo torsion
j	-1066370439424/5034679	j-invariant
L	2.1084888425323	L(r)(E,1)/r!
Ω	0.49589325483834	Real period
R	0.35432505247856	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	6448a1 25792t1 29016d1 80600i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3224c1

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	-1	-1	-2	+	0	7	4	6	-	-4	5	2	0	-6	-15	0	12	1	-2	0	14	-10	-1

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Quadratic twists for elliptic curve 3224c1

-4	8	-3	5	13	-31
6448a1	25792t1	29016d1	80600i1	41912b1	99944g1

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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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