Properties

Label 448.a
Number of curves 6
Conductor 448
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("448.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 448.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
448.a1 448f6 [0, 1, 0, -174753, 28059871] [2] 1152  
448.a2 448f5 [0, 1, 0, -10913, 436447] [2] 576  
448.a3 448f4 [0, 1, 0, -2273, 33439] [2] 384  
448.a4 448f2 [0, 1, 0, -673, -6945] [2] 128  
448.a5 448f1 [0, 1, 0, -33, -161] [2] 64 \(\Gamma_0(N)\)-optimal
448.a6 448f3 [0, 1, 0, 287, 3231] [2] 192  

Rank

sage: E.rank()
 

The elliptic curves in class 448.a have rank \(0\).

Modular form 448.2.a.a

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

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 18 & 6 \\ 2 & 1 & 6 & 18 & 9 & 3 \\ 3 & 6 & 1 & 3 & 6 & 2 \\ 9 & 18 & 3 & 1 & 2 & 6 \\ 18 & 9 & 6 & 2 & 1 & 3 \\ 6 & 3 & 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.