Properties

Label 54208.bj
Number of curves $4$
Conductor $54208$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bj1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 54208.bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
54208.bj1 54208bx4 \([0, 0, 0, -144716, 21189520]\) \(1443468546/7\) \(1625414303744\) \([2]\) \(163840\) \(1.5435\)  
54208.bj2 54208bx3 \([0, 0, 0, -28556, -1469424]\) \(11090466/2401\) \(557517106184192\) \([2]\) \(163840\) \(1.5435\)  
54208.bj3 54208bx2 \([0, 0, 0, -9196, 319440]\) \(740772/49\) \(5688950063104\) \([2, 2]\) \(81920\) \(1.1969\)  
54208.bj4 54208bx1 \([0, 0, 0, 484, 21296]\) \(432/7\) \(-203176787968\) \([2]\) \(40960\) \(0.85034\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 54208.bj have rank \(1\).

Complex multiplication

The elliptic curves in class 54208.bj do not have complex multiplication.

Modular form 54208.2.a.bj

sage: E.q_eigenform(10)
 
\(q - 2q^{5} - q^{7} - 3q^{9} + 2q^{13} + 6q^{17} - 8q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.