Properties

Label 487872.qh
Number of curves $2$
Conductor $487872$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("qh1")
 
E.isogeny_class()
 

Elliptic curves in class 487872.qh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
487872.qh1 487872qh1 \([0, 0, 0, -33396, 2438392]\) \(-84098304/3773\) \(-184801987206144\) \([]\) \(2211840\) \(1.5020\) \(\Gamma_0(N)\)-optimal
487872.qh2 487872qh2 \([0, 0, 0, 169884, 6612408]\) \(15185664/9317\) \(-332677520193199104\) \([]\) \(6635520\) \(2.0513\)  

Rank

sage: E.rank()
 

The elliptic curves in class 487872.qh have rank \(0\).

Complex multiplication

The elliptic curves in class 487872.qh do not have complex multiplication.

Modular form 487872.2.a.qh

sage: E.q_eigenform(10)
 
\(q + 3 q^{5} + q^{7} + 5 q^{13} + 6 q^{17} + q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.