Elliptic curve isogeny class with Cremona label 47753f (LMFDB label 47753.i)

• Label: 47753f
• Number of curves: $4$
• Conductor: $47753$
• CM: no
• Rank: $0$

Elliptic curves in class 47753f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
47753.i4	47753f1	$[1, -1, 0, -1931, 14440]$	$35937/17$	$376794139193$	$[2]$	$37440$	$0.91536$	$\Gamma_0(N)$-optimal
47753.i2	47753f2	$[1, -1, 0, -15976, -763653]$	$20346417/289$	$6405500366281$	$[2, 2]$	$74880$	$1.2619$
47753.i3	47753f3	$[1, -1, 0, -1931, -2069838]$	$-35937/83521$	$-1851189605855209$	$[2]$	$149760$	$1.6085$
47753.i1	47753f4	$[1, -1, 0, -254741, -49423960]$	$82483294977/17$	$376794139193$	$[2]$	$149760$	$1.6085$

Rank

The elliptic curves in class 47753f have rank $0$.

Complex multiplication

The elliptic curves in class 47753f do not have complex multiplication.

Modular form 47753.2.a.f

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.