Properties

Label 179088bh
Number of curves 2
Conductor 179088
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("179088.n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 179088bh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
179088.n1 179088bh1 [0, -1, 0, -2492896, -1514524928] [] 3161088 \(\Gamma_0(N)\)-optimal
179088.n2 179088bh2 [0, -1, 0, 13833344, 66885734272] [] 22127616  

Rank

sage: E.rank()
 

The elliptic curves in class 179088bh have rank \(0\).

Modular form 179088.2.a.n

sage: E.q_eigenform(10)
 
\( q - q^{3} - q^{5} - q^{7} + q^{9} + 2q^{11} - q^{13} + q^{15} + 4q^{17} + 8q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.