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
Δ	12298276002816 = 210 · 318 · 31	Discriminant
Eigenvalues	2- 3-  2  0 -4 -2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-8139,-226730]	[a1,a2,a3,a4,a6]
Generators	[-45:220:1]	Generators of the group modulo torsion
j	79874724388/16474671	j-invariant
L	3.3402534328063	L(r)(E,1)/r!
Ω	0.50993422908434	Real period
R	3.2751806432019	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	4464i3 17856r3 744b3 55800j4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2232k3

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 2232k3

-4	8	-3	5	-7	-31
4464i3	17856r3	744b3	55800j4	109368cb4	69192bj4

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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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