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Properties

Label 141267bl
Number of curves $2$
Conductor $141267$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bl1")
 
E.isogeny_class()
 

Elliptic curves in class 141267bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
141267.bq2 141267bl1 \([0, 1, 1, -2242, 43663]\) \(-28672/3\) \(-130463041107\) \([]\) \(169740\) \(0.87191\) \(\Gamma_0(N)\)-optimal
141267.bq1 141267bl2 \([0, 1, 1, -876752, -316528957]\) \(-1713910976512/1594323\) \(-69333409028945187\) \([]\) \(2206620\) \(2.1544\)  

Rank

sage: E.rank()
 

The elliptic curves in class 141267bl have rank \(0\).

Complex multiplication

The elliptic curves in class 141267bl do not have complex multiplication.

Modular form 141267.2.a.bl

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} + q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} + q^{9} + 4 q^{10} + 2 q^{11} + 2 q^{12} + q^{13} + 2 q^{15} - 4 q^{16} + 2 q^{18} - q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.