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Properties

Label 247254cx
Number of curves $2$
Conductor $247254$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("cx1")
 
E.isogeny_class()
 

Elliptic curves in class 247254cx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
247254.cx2 247254cx1 \([1, 0, 0, 967553, 449364089]\) \(596183/864\) \(-145171755973856386656\) \([]\) \(9631440\) \(2.5542\) \(\Gamma_0(N)\)-optimal
247254.cx1 247254cx2 \([1, 0, 0, -29321062, 61420346084]\) \(-16591834777/98304\) \(-16517319790803215548416\) \([]\) \(28894320\) \(3.1035\)  

Rank

sage: E.rank()
 

The elliptic curves in class 247254cx have rank \(0\).

Complex multiplication

The elliptic curves in class 247254cx do not have complex multiplication.

Modular form 247254.2.a.cx

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - 3 q^{5} + q^{6} + q^{8} + q^{9} - 3 q^{10} - 3 q^{11} + q^{12} + 4 q^{13} - 3 q^{15} + q^{16} + q^{18} - 4 q^{19} + O(q^{20})\) 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.