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Properties

Label 247962h
Number of curves $2$
Conductor $247962$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 247962h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
247962.h2 247962h1 \([1, 1, 0, -1884, -46020]\) \(-30664297/18876\) \(-455620752444\) \([2]\) \(414720\) \(0.93897\) \(\Gamma_0(N)\)-optimal
247962.h1 247962h2 \([1, 1, 0, -33674, -2392122]\) \(174958262857/33462\) \(807691333878\) \([2]\) \(829440\) \(1.2855\)  

Rank

sage: E.rank()
 

The elliptic curves in class 247962h have rank \(0\).

Complex multiplication

The elliptic curves in class 247962h do not have complex multiplication.

Modular form 247962.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + 2 q^{5} + q^{6} - 4 q^{7} - q^{8} + q^{9} - 2 q^{10} - q^{11} - q^{12} + q^{13} + 4 q^{14} - 2 q^{15} + q^{16} - q^{18} + 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.