Properties

Label 35520.k
Number of curves $6$
Conductor $35520$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("35520.k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 35520.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35520.k1 35520bq4 [0, -1, 0, -21824321, -39235457055] [2] 1327104  
35520.k2 35520bq6 [0, -1, 0, -19400001, 32752486881] [2] 2654208  
35520.k3 35520bq3 [0, -1, 0, -1876801, -110522399] [2, 2] 1327104  
35520.k4 35520bq2 [0, -1, 0, -1364801, -611975199] [2, 2] 663552  
35520.k5 35520bq1 [0, -1, 0, -54081, -16646175] [2] 331776 \(\Gamma_0(N)\)-optimal
35520.k6 35520bq5 [0, -1, 0, 7454399, -888744479] [2] 2654208  

Rank

sage: E.rank()
 

The elliptic curves in class 35520.k have rank \(0\).

Modular form 35520.2.a.k

sage: E.q_eigenform(10)
 
\( q - q^{3} - q^{5} + q^{9} + 4q^{11} + 2q^{13} + q^{15} + 2q^{17} + 4q^{19} + O(q^{20}) \)

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.