Properties

Label 141570.ed
Number of curves $2$
Conductor $141570$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("ed1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 141570.ed

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
141570.ed1 141570h2 \([1, -1, 1, -50117, -3855981]\) \(10779215329/1232010\) \(1591101452487690\) \([2]\) \(983040\) \(1.6492\)  
141570.ed2 141570h1 \([1, -1, 1, 4333, -305841]\) \(6967871/35100\) \(-45330525711900\) \([2]\) \(491520\) \(1.3026\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 141570.ed have rank \(0\).

Complex multiplication

The elliptic curves in class 141570.ed do not have complex multiplication.

Modular form 141570.2.a.ed

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} - 2q^{7} + q^{8} + q^{10} + q^{13} - 2q^{14} + q^{16} + 8q^{17} + 6q^{19} + O(q^{20})\)  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.