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Properties

Label 115542bw
Number of curves $2$
Conductor $115542$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bw1")
 
E.isogeny_class()
 

Elliptic curves in class 115542bw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115542.be2 115542bw1 \([1, -1, 1, -17429, 889179]\) \(6826561273/7074\) \(606709539954\) \([]\) \(284544\) \(1.1787\) \(\Gamma_0(N)\)-optimal
115542.be1 115542bw2 \([1, -1, 1, -63734, -5241603]\) \(333822098953/53954184\) \(4627441073400264\) \([]\) \(853632\) \(1.7280\)  

Rank

sage: E.rank()
 

The elliptic curves in class 115542bw have rank \(0\).

Complex multiplication

The elliptic curves in class 115542bw do not have complex multiplication.

Modular form 115542.2.a.bw

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - 3 q^{5} + q^{8} - 3 q^{10} - 3 q^{11} - 2 q^{13} + q^{16} - 3 q^{17} + 4 q^{19} + O(q^{20})\) 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.