Elliptic curve isogeny class with Cremona label 47040fa (LMFDB label 47040.cv)

• Label: 47040fa
• Number of curves: $4$
• Conductor: $47040$
• CM: no
• Rank: $0$

Elliptic curves in class 47040fa

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
47040.cv4	47040fa1	\([0, -1, 0, 180, -9918]\)	\(85184/5625\)	\(-42353640000\)	\([2]\)	\(36864\)	\(0.71870\)	\(\Gamma_0(N)\)-optimal
47040.cv3	47040fa2	\([0, -1, 0, -5945, -167943]\)	\(48228544/2025\)	\(975827865600\)	\([2, 2]\)	\(73728\)	\(1.0653\)
47040.cv2	47040fa3	\([0, -1, 0, -15745, 539617]\)	\(111980168/32805\)	\(126467291381760\)	\([2]\)	\(147456\)	\(1.4118\)
47040.cv1	47040fa4	\([0, -1, 0, -94145, -11087103]\)	\(23937672968/45\)	\(173480509440\)	\([2]\)	\(147456\)	\(1.4118\)

Rank

The elliptic curves in class 47040fa have rank \(0\).

Complex multiplication

The elliptic curves in class 47040fa do not have complex multiplication.

Modular form 47040.2.a.fa

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.