Elliptic curve isogeny class with LMFDB label 89232.bn (Cremona label 89232cq)

• Label: 89232.bn
• Number of curves: $4$
• Conductor: $89232$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 89232.bn have rank \(0\).

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 \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 89232.2.a.bn

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 89232.bn

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
89232.bn1	89232cq4	\([0, 1, 0, -13505184, 19098363636]\)	\(13778603383488553/13703976\)	\(270935960340824064\)	\([4]\)	\(3096576\)	\(2.6377\)
89232.bn2	89232cq3	\([0, 1, 0, -2040224, -710231820]\)	\(47504791830313/16490207448\)	\(326021454732793577472\)	\([2]\)	\(3096576\)	\(2.6377\)
89232.bn3	89232cq2	\([0, 1, 0, -850464, 293449716]\)	\(3440899317673/106007616\)	\(2095835197347201024\)	\([2, 2]\)	\(1548288\)	\(2.2912\)
89232.bn4	89232cq1	\([0, 1, 0, 14816, 15521780]\)	\(18191447/5271552\)	\(-104221796915478528\)	\([2]\)	\(774144\)	\(1.9446\)	\(\Gamma_0(N)\)-optimal