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Properties

Label 146523v
Number of curves $2$
Conductor $146523$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 146523v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
146523.bb2 146523v1 \([1, 0, 1, -489428, 133295879]\) \(-658489/9\) \(-177207809072015241\) \([]\) \(1372800\) \(2.1165\) \(\Gamma_0(N)\)-optimal
146523.bb1 146523v2 \([1, 0, 1, -3664093, -15009856171]\) \(-276301129/4782969\) \(-94175495261040851692281\) \([]\) \(9609600\) \(3.0895\)  

Rank

sage: E.rank()
 

The elliptic curves in class 146523v have rank \(0\).

Complex multiplication

The elliptic curves in class 146523v do not have complex multiplication.

Modular form 146523.2.a.v

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} - q^{4} + q^{5} + q^{6} - 2 q^{7} - 3 q^{8} + q^{9} + q^{10} + 2 q^{11} - q^{12} - 2 q^{14} + q^{15} - q^{16} + q^{18} - 6 q^{19} + O(q^{20})\) 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 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.