Properties

Label 48400ch
Number of curves $2$
Conductor $48400$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("ch1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 48400ch

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
48400.cx2 48400ch1 [0, -1, 0, -1008, 48512] [] 53760 \(\Gamma_0(N)\)-optimal
48400.cx1 48400ch2 [0, -1, 0, -1453008, -673679488] [] 591360  

Rank

sage: E.rank()
 

The elliptic curves in class 48400ch have rank \(1\).

Complex multiplication

The elliptic curves in class 48400ch do not have complex multiplication.

Modular form 48400.2.a.ch

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

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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.