Elliptic curve isogeny class with Cremona label 127050fi (LMFDB label 127050.fg)

• Label: 127050fi
• Number of curves: $4$
• Conductor: $127050$
• CM: no
• Rank: $1$

Elliptic curves in class 127050fi

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
127050.fg4	127050fi1	\([1, 1, 1, -293488, -223910719]\)	\(-100999381393/723148272\)	\(-20017207435821750000\)	\([2]\)	\(2949120\)	\(2.3867\)	\(\Gamma_0(N)\)-optimal
127050.fg3	127050fi2	\([1, 1, 1, -7613988, -8071486719]\)	\(1763535241378513/4612311396\)	\(127671734203268062500\)	\([2, 2]\)	\(5898240\)	\(2.7333\)
127050.fg2	127050fi3	\([1, 1, 1, -10608738, -1135645719]\)	\(4770223741048753/2740574865798\)	\(75860867966062041843750\)	\([2]\)	\(11796480\)	\(3.0799\)
127050.fg1	127050fi4	\([1, 1, 1, -121747238, -517105781719]\)	\(7209828390823479793/49509306\)	\(1370449306979156250\)	\([2]\)	\(11796480\)	\(3.0799\)

Rank

The elliptic curves in class 127050fi have rank \(1\).

Complex multiplication

The elliptic curves in class 127050fi do not have complex multiplication.

Modular form 127050.2.a.fi

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.