Elliptic curve isogeny class with Cremona label 27720j (LMFDB label 27720.t)

• Label: 27720j
• Number of curves: $4$
• Conductor: $27720$
• CM: no
• Rank: $0$

Elliptic curves in class 27720j

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
27720.t4	27720j1	$[0, 0, 0, -423, -8262]$	$-44851536/132055$	$-24644632320$	$[2]$	$16384$	$0.68090$	$\Gamma_0(N)$-optimal
27720.t3	27720j2	$[0, 0, 0, -9243, -341658]$	$116986321764/148225$	$110649369600$	$[2, 2]$	$32768$	$1.0275$
27720.t2	27720j3	$[0, 0, 0, -11763, -140562]$	$120564797922/64054375$	$95632669440000$	$[2]$	$65536$	$1.3740$
27720.t1	27720j4	$[0, 0, 0, -147843, -21880098]$	$239369344910082/385$	$574801920$	$[2]$	$65536$	$1.3740$

Rank

The elliptic curves in class 27720j have rank $0$.

Complex multiplication

The elliptic curves in class 27720j do not have complex multiplication.

Modular form 27720.2.a.j

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.