Properties

Label 226512.fd
Number of curves $6$
Conductor $226512$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("226512.fd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 226512.fd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
226512.fd1 226512cq4 [0, 0, 0, -119598699, -503428498342] [2] 15728640  
226512.fd2 226512cq5 [0, 0, 0, -52429179, 141492303722] [2] 31457280  
226512.fd3 226512cq3 [0, 0, 0, -8259339, -6114467590] [2, 2] 15728640  
226512.fd4 226512cq2 [0, 0, 0, -7475259, -7865318230] [2, 2] 7864320  
226512.fd5 226512cq1 [0, 0, 0, -418539, -149500582] [2] 3932160 \(\Gamma_0(N)\)-optimal
226512.fd6 226512cq6 [0, 0, 0, 23365221, -41666797942] [2] 31457280  

Rank

sage: E.rank()
 

The elliptic curves in class 226512.fd have rank \(0\).

Modular form 226512.2.a.fd

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

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.