Elliptic curve isogeny class with LMFDB label 127050.i (Cremona label 127050e)

• Label: 127050.i
• Number of curves: $4$
• Conductor: $127050$
• CM: no
• Rank: $0$

Elliptic curves in class 127050.i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
127050.i1	127050e4	\([1, 1, 0, -78781650, -269157123000]\)	\(1953542217204454969/170843779260\)	\(4729065256712888437500\)	\([2]\)	\(14745600\)	\(3.2003\)
127050.i2	127050e3	\([1, 1, 0, -28566650, 55751472000]\)	\(93137706732176569/5369647977540\)	\(148635295949042811562500\)	\([2]\)	\(14745600\)	\(3.2003\)
127050.i3	127050e2	\([1, 1, 0, -5274150, -3574525500]\)	\(586145095611769/140040608400\)	\(3876413754026756250000\)	\([2, 2]\)	\(7372800\)	\(2.8537\)
127050.i4	127050e1	\([1, 1, 0, 775850, -349875500]\)	\(1865864036231/2993760000\)	\(-82869194677500000000\)	\([2]\)	\(3686400\)	\(2.5071\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 127050.i have rank \(0\).

Complex multiplication

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

Modular form 127050.2.a.i

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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.