Elliptic curve isogeny class with LMFDB label 169065.bi (Cremona label 169065x)

• Label: 169065.bi
• Number of curves: $8$
• Conductor: $169065$
• CM: no
• Rank: $0$

Elliptic curves in class 169065.bi

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
169065.bi1	169065x7	$[1, -1, 0, -338130054, 2393255770753]$	$242970740812818720001/24375$	$428909515149375$	$[2]$	$15728640$	$3.1553$
169065.bi2	169065x5	$[1, -1, 0, -21133179, 37398395128]$	$59319456301170001/594140625$	$10454669431766015625$	$[2, 2]$	$7864320$	$2.8088$
169065.bi3	169065x8	$[1, -1, 0, -20625984, 39278364115]$	$-55150149867714721/5950927734375$	$-104714237097015380859375$	$[2]$	$15728640$	$3.1553$
169065.bi4	169065x3	$[1, -1, 0, -1352574, 555040255]$	$15551989015681/1445900625$	$25442483529145775625$	$[2, 2]$	$3932160$	$2.4622$
169065.bi5	169065x2	$[1, -1, 0, -299169, -53195792]$	$168288035761/27720225$	$487773057008475225$	$[2, 2]$	$1966080$	$2.1156$
169065.bi6	169065x1	$[1, -1, 0, -286164, -58847765]$	$147281603041/5265$	$92644455272265$	$[2]$	$983040$	$1.7690$	$\Gamma_0(N)$-optimal
169065.bi7	169065x4	$[1, -1, 0, 546156, -299861627]$	$1023887723039/2798036865$	$-49235061954347783865$	$[2]$	$3932160$	$2.4622$
169065.bi8	169065x6	$[1, -1, 0, 1573551, 2626151530]$	$24487529386319/183539412225$	$-3229612320337477767225$	$[2]$	$7864320$	$2.8088$

Rank

The elliptic curves in class 169065.bi have rank $0$.

Complex multiplication

The elliptic curves in class 169065.bi do not have complex multiplication.

Modular form 169065.2.a.bi

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.

$\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 16 & 16 & 8 \\ 2 & 1 & 2 & 2 & 4 & 8 & 8 & 4 \\ 4 & 2 & 1 & 4 & 8 & 16 & 16 & 8 \\ 4 & 2 & 4 & 1 & 2 & 4 & 4 & 2 \\ 8 & 4 & 8 & 2 & 1 & 2 & 2 & 4 \\ 16 & 8 & 16 & 4 & 2 & 1 & 4 & 8 \\ 16 & 8 & 16 & 4 & 2 & 4 & 1 & 8 \\ 8 & 4 & 8 & 2 & 4 & 8 & 8 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with LMFDB labels.