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	2232g	Isogeny class
Conductor	2232	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	256	Modular degree for the optimal curve
Δ	-361584 = -1 · 24 · 36 · 31	Discriminant
Eigenvalues	2+ 3-  3 -3 -2 -4  0  1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,9,27]	[a1,a2,a3,a4,a6]
Generators	[3:9:1]	Generators of the group modulo torsion
j	6912/31	j-invariant
L	3.3246204537879	L(r)(E,1)/r!
Ω	2.1650305878485	Real period
R	0.3838999403112	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	4464e1 17856bj1 248c1 55800cb1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2232g1

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
+	-	3	-3	-2	-4	0	1	-4	6	-	-10	-7	-10	-12	4	-3	12	-12	13	2	6	-6	10	1

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Quadratic twists for elliptic curve 2232g1

-4	8	-3	5	-7	-31
4464e1	17856bj1	248c1	55800cb1	109368p1	69192t1

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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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