Elliptic curve isogeny class with Cremona label 9792bs (LMFDB label 9792.i)

• Label: 9792bs
• Number of curves: $4$
• Conductor: $9792$
• CM: no
• Rank: $1$

Elliptic curves in class 9792bs

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
9792.i4	9792bs1	$[0, 0, 0, -396, 1296]$	$35937/17$	$3248750592$	$[2]$	$4096$	$0.51924$	$\Gamma_0(N)$-optimal
9792.i2	9792bs2	$[0, 0, 0, -3276, -71280]$	$20346417/289$	$55228760064$	$[2, 2]$	$8192$	$0.86582$
9792.i1	9792bs3	$[0, 0, 0, -52236, -4595184]$	$82483294977/17$	$3248750592$	$[2]$	$16384$	$1.2124$
9792.i3	9792bs4	$[0, 0, 0, -396, -192240]$	$-35937/83521$	$-15961111658496$	$[2]$	$16384$	$1.2124$

Rank

The elliptic curves in class 9792bs have rank $1$.

Complex multiplication

The elliptic curves in class 9792bs do not have complex multiplication.

Modular form 9792.2.a.bs

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.