Elliptic curve isogeny class with Cremona label 89232cb (LMFDB label 89232.bt)

• Label: 89232cb
• Number of curves: $4$
• Conductor: $89232$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 89232cb have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(11\)	\(1 - T\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 4 T + 29 T^{2}\)	1.29.ae
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 89232cb do not have complex multiplication.

Modular form 89232.2.a.cb

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 89232cb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
89232.bt3	89232cb1	\([0, 1, 0, -2885224, -1884795340]\)	\(134351465835313/205590528\)	\(4064650079703662592\)	\([2]\)	\(2322432\)	\(2.4703\)	\(\Gamma_0(N)\)-optimal
89232.bt2	89232cb2	\([0, 1, 0, -3750504, -661981644]\)	\(295102348042033/161237583936\)	\(3187765335165092757504\)	\([2, 2]\)	\(4644864\)	\(2.8169\)
89232.bt4	89232cb3	\([0, 1, 0, 14528536, -5202495180]\)	\(17154149157653327/10519679024712\)	\(-207980467788149162016768\)	\([2]\)	\(9289728\)	\(3.1635\)
89232.bt1	89232cb4	\([0, 1, 0, -35874024, 82152452916]\)	\(258252149810350513/1938176193096\)	\(38318924973758507679744\)	\([2]\)	\(9289728\)	\(3.1635\)