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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)
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.