Cremona's table of elliptic curves

23232 = 2⁶ · 3 · 11²

Field	Data	Notes
Atkin-Lehner	2+ 3+ 11-	Signs for the Atkin-Lehner involutions
Class	23232m	Isogeny class
Conductor	23232	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	18432	Modular degree for the optimal curve
Δ	-10277093376 = -1 · 220 · 34 · 112	Discriminant
Eigenvalues	2+ 3+  1 -4 11- -5 -7  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-865,11233]	[a1,a2,a3,a4,a6]
Generators	[-17:144:1] [9:64:1]	Generators of the group modulo torsion
j	-2259169/324	j-invariant
L	6.4182897862995	L(r)(E,1)/r!
Ω	1.243671993945	Real period
R	0.64509470921064	Regulator
r	2	Rank of the group of rational points
S	1.0000000000001	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	23232dn1 726d1 69696cc1 23232l1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 23232m1

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	-4	-	-5	-7	0	0	7	-8	5	-11	-8	4	5	0	-2	-12	-16	6	-4	-8	-17	-5

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Quadratic twists for elliptic curve 23232m1

-4	8	-3	-11
23232dn1	726d1	69696cc1	23232l1

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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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