Elliptic curve isogeny class with Cremona label 159201t (LMFDB label 159201.t)

• Label: 159201t
• Number of curves: $2$
• Conductor: $159201$
• CM: $\Q(\sqrt{-19})$
• Rank: $1$

Elliptic curves in class 159201t

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
159201.t2	159201t1	$[0, 0, 1, -16758, 835805]$	$-884736$	$-588269823939$	$[]$	$211200$	$1.1721$	$\Gamma_0(N)$-optimal	$-19$
159201.t1	159201t2	$[0, 0, 1, -6049638, -5732788210]$	$-884736$	$-27675672132925145259$	$[]$	$4012800$	$2.6443$		$-19$

Rank

The elliptic curves in class 159201t have rank $1$.

Complex multiplication

Each elliptic curve in class 159201t has complex multiplication by an order in the imaginary quadratic field $\Q(\sqrt{-19})$.

Modular form 159201.2.a.t

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.

$\left(\begin{array}{rr} 1 & 19 \\ 19 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.