Cremona's table of elliptic curves

2232 = 2³ · 3² · 31

Field	Data	Notes
Atkin-Lehner	2- 3- 31+	Signs for the Atkin-Lehner involutions
Class	2232k	Isogeny class
Conductor	2232	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	960	Modular degree for the optimal curve
Δ	9762768 = 24 · 39 · 31	Discriminant
Eigenvalues	2- 3-  2  0 -4 -2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-2514,48517]	[a1,a2,a3,a4,a6]
Generators	[54:265:1]	Generators of the group modulo torsion
j	150651000832/837	j-invariant
L	3.3402534328063	L(r)(E,1)/r!
Ω	2.0397369163374	Real period
R	3.2751806432019	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	4464i1 17856r1 744b1 55800j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2232k1

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

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Quadratic twists for elliptic curve 2232k1

-4	8	-3	5	-7	-31
4464i1	17856r1	744b1	55800j1	109368cb1	69192bj1

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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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