Properties

Label 114240ha
Number of curves $2$
Conductor $114240$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("ha1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 114240ha

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
114240.dr2 114240ha1 \([0, -1, 0, 5215, -174783]\) \(59822347031/83966400\) \(-22011287961600\) \([2]\) \(221184\) \(1.2458\) \(\Gamma_0(N)\)-optimal
114240.dr1 114240ha2 \([0, -1, 0, -33185, -1703103]\) \(15417797707369/4080067320\) \(1069565167534080\) \([2]\) \(442368\) \(1.5924\)  

Rank

sage: E.rank()
 

The elliptic curves in class 114240ha have rank \(0\).

Complex multiplication

The elliptic curves in class 114240ha do not have complex multiplication.

Modular form 114240.2.a.ha

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} - q^{7} + q^{9} + 2q^{11} + 2q^{13} - q^{15} + q^{17} - 4q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.