Properties

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

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 141570.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
141570.k1 141570dr2 \([1, -1, 0, -340761735, -719181065795]\) \(3388383326345613179401/1787816842064922240\) \(2308908185965578891435730560\) \([2]\) \(72253440\) \(3.9421\)  
141570.k2 141570dr1 \([1, -1, 0, 80899065, -87786183875]\) \(45338857965533777399/28814396538470400\) \(-37212870175498997854617600\) \([2]\) \(36126720\) \(3.5955\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 141570.2.a.k

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