Properties

Label 179088.n
Number of curves $2$
Conductor $179088$
CM no
Rank $0$
Graph

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

Elliptic curves in class 179088.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
179088.n1 179088bh1 \([0, -1, 0, -2492896, -1514524928]\) \(-418288977642645996769/122877464621184\) \(-503306095088369664\) \([]\) \(3161088\) \(2.3757\) \(\Gamma_0(N)\)-optimal
179088.n2 179088bh2 \([0, -1, 0, 13833344, 66885734272]\) \(71473535169369644529791/513262758348672548034\) \(-2102324258196162756747264\) \([]\) \(22127616\) \(3.3487\)  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 179088.n do not have complex multiplication.

Modular form 179088.2.a.n

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.