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.