Properties

Label 141570.j
Number of curves $2$
Conductor $141570$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 141570.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
141570.j1 141570ew2 \([1, -1, 0, -86242470, 154338972596]\) \(2034416504287874043/882294347833600\) \(30765282015334651432876800\) \([2]\) \(39321600\) \(3.5869\)  
141570.j2 141570ew1 \([1, -1, 0, 18301530, 17867234996]\) \(19441890357117957/15208161280000\) \(-530303035333663088640000\) \([2]\) \(19660800\) \(3.2403\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 141570.j have rank \(1\).

Complex multiplication

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

Modular form 141570.2.a.j

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