Elliptic curve isogeny class with Cremona label 206310ce (LMFDB label 206310.n)

• Label: 206310ce
• Number of curves: $4$
• Conductor: $206310$
• CM: no
• Rank: $1$

Elliptic curves in class 206310ce

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
206310.n3	206310ce1	$[1, 1, 0, -7152, -228816]$	$273359449/9360$	$1385615921040$	$[2]$	$394240$	$1.1016$	$\Gamma_0(N)$-optimal
206310.n2	206310ce2	$[1, 1, 0, -17732, 590076]$	$4165509529/1368900$	$202646328452100$	$[2, 2]$	$788480$	$1.4482$
206310.n1	206310ce3	$[1, 1, 0, -255782, 49675986]$	$12501706118329/2570490$	$380524772315610$	$[2]$	$1576960$	$1.7948$
206310.n4	206310ce4	$[1, 1, 0, 51038, 4124854]$	$99317171591/106616250$	$-15783031350596250$	$[2]$	$1576960$	$1.7948$

Rank

The elliptic curves in class 206310ce have rank $1$.

Complex multiplication

The elliptic curves in class 206310ce do not have complex multiplication.

Modular form 206310.2.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.

$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.