Properties

Label 58800.bx
Number of curves $4$
Conductor $58800$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bx1")
 
E.isogeny_class()
 

Elliptic curves in class 58800.bx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
58800.bx1 58800fj4 \([0, -1, 0, -2205408, -1259786688]\) \(157551496201/13125\) \(98825160000000000\) \([2]\) \(1179648\) \(2.3049\)  
58800.bx2 58800fj2 \([0, -1, 0, -147408, -16754688]\) \(47045881/11025\) \(83013134400000000\) \([2, 2]\) \(589824\) \(1.9583\)  
58800.bx3 58800fj1 \([0, -1, 0, -49408, 4021312]\) \(1771561/105\) \(790601280000000\) \([2]\) \(294912\) \(1.6117\) \(\Gamma_0(N)\)-optimal
58800.bx4 58800fj3 \([0, -1, 0, 342592, -104954688]\) \(590589719/972405\) \(-7321758454080000000\) \([2]\) \(1179648\) \(2.3049\)  

Rank

sage: E.rank()
 

The elliptic curves in class 58800.bx have rank \(1\).

Complex multiplication

The elliptic curves in class 58800.bx do not have complex multiplication.

Modular form 58800.2.a.bx

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{9} - 6 q^{13} + 2 q^{17} - 8 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().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 LMFDB 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

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.