Properties

Label 444675.bj
Number of curves $2$
Conductor $444675$
CM no
Rank $0$
Graph

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

Elliptic curves in class 444675.bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
444675.bj1 444675bj2 [0, 1, 1, -3970997158, -1820911366584656] [] 4147200000  
444675.bj2 444675bj1 [0, 1, 1, -1325180908, 21744015290344] [] 829440000 \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 444675.bj1.

Rank

sage: E.rank()
 

The elliptic curves in class 444675.bj have rank \(0\).

Complex multiplication

The elliptic curves in class 444675.bj do not have complex multiplication.

Modular form 444675.2.a.bj

sage: E.q_eigenform(10)
 
\( q - 2q^{2} + q^{3} + 2q^{4} - 2q^{6} + q^{9} + 2q^{12} + 6q^{13} - 4q^{16} + 7q^{17} - 2q^{18} - 5q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.