Properties

Label 13050bi
Number of curves $2$
Conductor $13050$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bi1")
 
E.isogeny_class()
 

Elliptic curves in class 13050bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13050.bn2 13050bi1 \([1, -1, 1, 1120, -24253]\) \(13651919/29696\) \(-338256000000\) \([]\) \(16800\) \(0.89647\) \(\Gamma_0(N)\)-optimal
13050.bn1 13050bi2 \([1, -1, 1, -102380, 12719747]\) \(-10418796526321/82044596\) \(-934539226312500\) \([]\) \(84000\) \(1.7012\)  

Rank

sage: E.rank()
 

The elliptic curves in class 13050bi have rank \(0\).

Complex multiplication

The elliptic curves in class 13050bi do not have complex multiplication.

Modular form 13050.2.a.bi

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + 2 q^{7} + q^{8} + 3 q^{11} + q^{13} + 2 q^{14} + q^{16} + 8 q^{17} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.