Elliptic curve isogeny class with LMFDB label 89232.bh (Cremona label 89232br)

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

Rank

The elliptic curves in class 89232.bh 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 \(\mathbb{F}_p\)
\(5\)	\( 1 - 4 T + 5 T^{2}\)	1.5.ae
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 - 10 T + 29 T^{2}\)	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 89232.2.a.bh

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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 89232.bh

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
89232.bh1	89232br3	\([0, -1, 0, -27215816, 54657812208]\)	\(112763292123580561/1932612\)	\(38208917483962368\)	\([2]\)	\(5184000\)	\(2.7235\)
89232.bh2	89232br4	\([0, -1, 0, -27188776, 54771812848]\)	\(-112427521449300721/466873642818\)	\(-9230376554564434993152\)	\([2]\)	\(10368000\)	\(3.0700\)
89232.bh3	89232br1	\([0, -1, 0, -121736, -11876112]\)	\(10091699281/2737152\)	\(54115163783036928\)	\([2]\)	\(1036800\)	\(1.9188\)	\(\Gamma_0(N)\)-optimal
89232.bh4	89232br2	\([0, -1, 0, 310904, -77637392]\)	\(168105213359/228637728\)	\(-4520307274751803392\)	\([2]\)	\(2073600\)	\(2.2653\)