Properties

Label 141610.v
Number of curves $2$
Conductor $141610$
CM no
Rank $1$
Graph

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

Elliptic curves in class 141610.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
141610.v1 141610cc2 \([1, -1, 0, -9319, -341517]\) \(154854153/1250\) \(722511921250\) \([2]\) \(276480\) \(1.1026\)  
141610.v2 141610cc1 \([1, -1, 0, -989, 3345]\) \(185193/100\) \(57800953700\) \([2]\) \(138240\) \(0.75607\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 141610.v have rank \(1\).

Complex multiplication

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

Modular form 141610.2.a.v

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.