Elliptic curve isogeny class with Cremona label 141120lf (LMFDB label 141120.w)

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

Elliptic curves in class 141120lf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
141120.w4	141120lf1	\([0, 0, 0, -509943, 211341508]\)	\(-2671731885376/1969120125\)	\(-10808562873874248000\)	\([2]\)	\(2359296\)	\(2.3517\)	\(\Gamma_0(N)\)-optimal
141120.w3	141120lf2	\([0, 0, 0, -9261588, 10846340512]\)	\(250094631024064/62015625\)	\(21785966991936000000\)	\([2, 2]\)	\(4718592\)	\(2.6982\)
141120.w1	141120lf3	\([0, 0, 0, -148176588, 694252574512]\)	\(128025588102048008/7875\)	\(22131775991808000\)	\([2]\)	\(9437184\)	\(3.0448\)
141120.w2	141120lf4	\([0, 0, 0, -10372908, 8080042768]\)	\(43919722445768/15380859375\)	\(43226124984000000000000\)	\([2]\)	\(9437184\)	\(3.0448\)

Rank

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

Complex multiplication

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

Modular form 141120.2.a.lf

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.