Elliptic curve isogeny class with Cremona label 84474ce (LMFDB label 84474.by)

• Label: 84474ce
• Number of curves: $2$
• Conductor: $84474$
• CM: no
• Rank: $1$

Elliptic curves in class 84474ce

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
84474.by2	84474ce1	$[1, -1, 1, -8732, 482527]$	$-2146689/1664$	$-57069288222336$	$[]$	$183456$	$1.3384$	$\Gamma_0(N)$-optimal
84474.by1	84474ce2	$[1, -1, 1, -691022, -242412713]$	$-1064019559329/125497034$	$-4304102406486959466$	$[]$	$1284192$	$2.3113$

Rank

The elliptic curves in class 84474ce have rank $1$.

Complex multiplication

The elliptic curves in class 84474ce do not have complex multiplication.

Modular form 84474.2.a.ce

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.

$\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.