Properties

Label 2448n
Number of curves 6
Conductor 2448
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("2448.p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2448n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2448.p5 2448n1 [0, 0, 0, -4899, 122402] [2] 3072 \(\Gamma_0(N)\)-optimal
2448.p4 2448n2 [0, 0, 0, -16419, -667870] [2, 2] 6144  
2448.p2 2448n3 [0, 0, 0, -249699, -48023710] [2, 2] 12288  
2448.p6 2448n4 [0, 0, 0, 32541, -3889438] [2] 12288  
2448.p1 2448n5 [0, 0, 0, -3995139, -3073590142] [2] 24576  
2448.p3 2448n6 [0, 0, 0, -236739, -53231038] [2] 24576  

Rank

sage: E.rank()
 

The elliptic curves in class 2448n have rank \(1\).

Modular form 2448.2.a.p

sage: E.q_eigenform(10)
 
\( q + 2q^{5} - 4q^{11} - 2q^{13} - q^{17} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.