Properties

Label 136242bq
Number of curves $2$
Conductor $136242$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bq1")
 
E.isogeny_class()
 

Elliptic curves in class 136242bq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
136242.t2 136242bq1 \([1, -1, 0, 3627, 7477]\) \(109503/64\) \(-3083564096064\) \([]\) \(275184\) \(1.0858\) \(\Gamma_0(N)\)-optimal
136242.t1 136242bq2 \([1, -1, 0, -46833, -4247983]\) \(-35937/4\) \(-1264454002142244\) \([]\) \(825552\) \(1.6351\)  

Rank

sage: E.rank()
 

The elliptic curves in class 136242bq have rank \(1\).

Complex multiplication

The elliptic curves in class 136242bq do not have complex multiplication.

Modular form 136242.2.a.bq

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + 3 q^{5} - 4 q^{7} - q^{8} - 3 q^{10} - q^{13} + 4 q^{14} + q^{16} - 3 q^{17} + 4 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.