Elliptic curve isogeny class with Cremona label 158400kt (LMFDB label 158400.er)

• Label: 158400kt
• Number of curves: $4$
• Conductor: $158400$
• CM: no
• Rank: $1$

Elliptic curves in class 158400kt

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
158400.er4	158400kt1	\([0, 0, 0, 196800, 123469000]\)	\(72268906496/606436875\)	\(-7073479710000000000\)	\([2]\)	\(1769472\)	\(2.2983\)	\(\Gamma_0(N)\)-optimal
158400.er3	158400kt2	\([0, 0, 0, -2840700, 1696894000]\)	\(13584145739344/1195803675\)	\(223165665043200000000\)	\([2]\)	\(3538944\)	\(2.6448\)
158400.er2	158400kt3	\([0, 0, 0, -14059200, 20306401000]\)	\(-26348629355659264/24169921875\)	\(-281917968750000000000\)	\([2]\)	\(5308416\)	\(2.8476\)
158400.er1	158400kt4	\([0, 0, 0, -224996700, 1299009526000]\)	\(6749703004355978704/5671875\)	\(1058508000000000000\)	\([2]\)	\(10616832\)	\(3.1942\)

Rank

The elliptic curves in class 158400kt have rank \(1\).

Complex multiplication

The elliptic curves in class 158400kt do not have complex multiplication.

Modular form 158400.2.a.kt

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.