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	2232h	Isogeny class
Conductor	2232	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	480	Modular degree for the optimal curve
Δ	9762768 = 24 · 39 · 31	Discriminant
Eigenvalues	2- 3+  0  0 -4  2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-270,1701]	[a1,a2,a3,a4,a6]
Generators	[-18:27:1]	Generators of the group modulo torsion
j	6912000/31	j-invariant
L	3.0705864661248	L(r)(E,1)/r!
Ω	2.308365942362	Real period
R	1.3301991723994	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	4464a1 17856e1 2232a1 55800e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2232h1

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
-	+	0	0	-4	2	-6	4	4	6	-	-10	-8	-4	-6	-10	-6	6	12	2	14	0	-12	-10	-14

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Quadratic twists for elliptic curve 2232h1

-4	8	-3	5	-7	-31
4464a1	17856e1	2232a1	55800e1	109368be1	69192ba1

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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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