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.