Elliptic curve isogeny class with Cremona label 141120mt (LMFDB label 141120.gs)

• Label: 141120mt
• Number of curves: $4$
• Conductor: $141120$
• CM: no
• Rank: $1$

Elliptic curves in class 141120mt

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
141120.gs4	141120mt1	\([0, 0, 0, -509943, -211341508]\)	\(-2671731885376/1969120125\)	\(-10808562873874248000\)	\([2]\)	\(2359296\)	\(2.3517\)	\(\Gamma_0(N)\)-optimal
141120.gs3	141120mt2	\([0, 0, 0, -9261588, -10846340512]\)	\(250094631024064/62015625\)	\(21785966991936000000\)	\([2, 2]\)	\(4718592\)	\(2.6982\)
141120.gs2	141120mt3	\([0, 0, 0, -10372908, -8080042768]\)	\(43919722445768/15380859375\)	\(43226124984000000000000\)	\([2]\)	\(9437184\)	\(3.0448\)
141120.gs1	141120mt4	\([0, 0, 0, -148176588, -694252574512]\)	\(128025588102048008/7875\)	\(22131775991808000\)	\([2]\)	\(9437184\)	\(3.0448\)

Rank

The elliptic curves in class 141120mt have rank \(1\).

Complex multiplication

The elliptic curves in class 141120mt do not have complex multiplication.

Modular form 141120.2.a.mt

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.