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Properties

Label 141610.a
Number of curves $2$
Conductor $141610$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 141610.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
141610.a1 141610bm2 \([1, -1, 0, -6179350, 5914200886]\) \(-45145776875761017/2441406250\) \(-1411156096191406250\) \([]\) \(9345024\) \(2.5494\)  
141610.a2 141610bm1 \([1, -1, 0, -6820, -317360]\) \(-60698457/40960\) \(-23675270635520\) \([]\) \(718848\) \(1.2669\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 141610.a have rank \(0\).

Complex multiplication

The elliptic curves in class 141610.a do not have complex multiplication.

Modular form 141610.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} - 3 q^{3} + q^{4} - q^{5} + 3 q^{6} - q^{8} + 6 q^{9} + q^{10} - 2 q^{11} - 3 q^{12} - q^{13} + 3 q^{15} + q^{16} - 6 q^{18} + 7 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.