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	2232c	Isogeny class
Conductor	2232	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	-23141376 = -1 · 210 · 36 · 31	Discriminant
Eigenvalues	2+ 3- -2  0 -2  4 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,69,70]	[a1,a2,a3,a4,a6]
j	48668/31	j-invariant
L	1.3300713407139	L(r)(E,1)/r!
Ω	1.3300713407139	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	4464j1 17856p1 248b1 55800bp1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2232c1

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

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Quadratic twists for elliptic curve 2232c1

-4	8	-3	5	-7	-31
4464j1	17856p1	248b1	55800bp1	109368u1	69192m1

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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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