Properties

Label 2448q
Number of curves 4
Conductor 2448
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("2448.k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2448q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2448.k4 2448q1 [0, 0, 0, -435, 2162] [2] 1152 \(\Gamma_0(N)\)-optimal
2448.k3 2448q2 [0, 0, 0, -6195, 187634] [2] 2304  
2448.k2 2448q3 [0, 0, 0, -14835, -695374] [2] 3456  
2448.k1 2448q4 [0, 0, 0, -16275, -552238] [2] 6912  

Rank

sage: E.rank()
 

The elliptic curves in class 2448q have rank \(0\).

Modular form 2448.2.a.k

sage: E.q_eigenform(10)
 
\( q + 4q^{7} + 6q^{11} + 2q^{13} + q^{17} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.