Elliptic curve isogeny class with Cremona label 381150pk (LMFDB label 381150.pk)

• Label: 381150pk
• Number of curves: $4$
• Conductor: $381150$
• CM: no
• Rank: $0$

Elliptic curves in class 381150pk

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
381150.pk3	381150pk1	\([1, -1, 1, -141230, -17865603]\)	\(416832723/56000\)	\(41853128625000000\)	\([2]\)	\(3317760\)	\(1.9169\)	\(\Gamma_0(N)\)-optimal
381150.pk4	381150pk2	\([1, -1, 1, 221770, -94821603]\)	\(1613964717/6125000\)	\(-4577685943359375000\)	\([2]\)	\(6635520\)	\(2.2634\)
381150.pk1	381150pk3	\([1, -1, 1, -2863730, 1863684397]\)	\(4767078987/6860\)	\(3737589019034062500\)	\([2]\)	\(9953280\)	\(2.4662\)
381150.pk2	381150pk4	\([1, -1, 1, -2046980, 2948328397]\)	\(-1740992427/5882450\)	\(-3204982583821708593750\)	\([2]\)	\(19906560\)	\(2.8128\)

Rank

The elliptic curves in class 381150pk have rank \(0\).

Complex multiplication

The elliptic curves in class 381150pk do not have complex multiplication.

Modular form 381150.2.a.pk

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.