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	23232cf	Isogeny class
Conductor	23232	Conductor
∏ cp	20	Product of Tamagawa factors cp
Δ	1706859170463744 = 215 · 35 · 118	Discriminant
Eigenvalues	2+ 3- -2  4 11- -2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-151798049,719808335871]	[a1,a2,a3,a4,a6]
Generators	[68762:1791405:8]	Generators of the group modulo torsion
j	6663712298552914184/29403	j-invariant
L	6.1962084581074	L(r)(E,1)/r!
Ω	0.22627253598377	Real period
R	5.4767658223903	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	23232v4 11616d3 69696ck4 2112n3	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 23232cf4

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	4	-	-2	-2	-4	0	-6	-4	2	6	4	8	6	12	-10	4	0	-10	12	-12	10	18

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Quadratic twists for elliptic curve 23232cf4

-4	8	-3	-11
23232v4	11616d3	69696ck4	2112n3

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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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