Elliptic curve isogeny class with Cremona label 81600im (LMFDB label 81600.hj)

• Label: 81600im
• Number of curves: $4$
• Conductor: $81600$
• CM: no
• Rank: $0$

Elliptic curves in class 81600im

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
81600.hj3	81600im1	$[0, 1, 0, -95133, -9290637]$	$5951163357184/1129312125$	$18068994000000000$	$[2]$	$663552$	$1.8370$	$\Gamma_0(N)$-optimal
81600.hj2	81600im2	$[0, 1, 0, -459633, 111358863]$	$41948679809104/3291890625$	$842724000000000000$	$[2, 2]$	$1327104$	$2.1836$
81600.hj4	81600im3	$[0, 1, 0, 458367, 501508863]$	$10400706415004/112060546875$	$-114750000000000000000$	$[2]$	$2654208$	$2.5301$
81600.hj1	81600im4	$[0, 1, 0, -7209633, 7448608863]$	$40472803590982276/281883375$	$288648576000000000$	$[2]$	$2654208$	$2.5301$

Rank

The elliptic curves in class 81600im have rank $0$.

Complex multiplication

The elliptic curves in class 81600im do not have complex multiplication.

Modular form 81600.2.a.im

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.