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	2232f	Isogeny class
Conductor	2232	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	-28146060144 = -1 · 24 · 310 · 313	Discriminant
Eigenvalues	2+ 3- -1 -3  2  4  4 -7	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1263,-19069]	[a1,a2,a3,a4,a6]
Generators	[55:279:1]	Generators of the group modulo torsion
j	-19102326016/2413071	j-invariant
L	2.8424181311003	L(r)(E,1)/r!
Ω	0.39761476833429	Real period
R	0.59572278611278	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	4464c1 17856z1 744f1 55800ca1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2232f1

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	-3	2	4	4	-7	-4	6	-	-6	-3	-2	12	-4	-7	-8	-4	1	-2	-14	-14	6	-7

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Quadratic twists for elliptic curve 2232f1

-4	8	-3	5	-7	-31
4464c1	17856z1	744f1	55800ca1	109368l1	69192k1

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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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