Elliptic curve isogeny class with Cremona label 19110bh (LMFDB label 19110.bg)

• Label: 19110bh
• Number of curves: $4$
• Conductor: $19110$
• CM: no
• Rank: $1$

Elliptic curves in class 19110bh

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
19110.bg3	19110bh1	$[1, 0, 1, -663, -6422]$	$273359449/9360$	$1101194640$	$[2]$	$12288$	$0.50684$	$\Gamma_0(N)$-optimal
19110.bg2	19110bh2	$[1, 0, 1, -1643, 16706]$	$4165509529/1368900$	$161049716100$	$[2, 2]$	$24576$	$0.85341$
19110.bg1	19110bh3	$[1, 0, 1, -23693, 1401446]$	$12501706118329/2570490$	$302415578010$	$[2]$	$49152$	$1.2000$
19110.bg4	19110bh4	$[1, 0, 1, 4727, 116078]$	$99317171591/106616250$	$-12543295196250$	$[2]$	$49152$	$1.2000$

Rank

The elliptic curves in class 19110bh have rank $1$.

Complex multiplication

The elliptic curves in class 19110bh do not have complex multiplication.

Modular form 19110.2.a.bh

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.