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SageMath
E = EllipticCurve("dh1")
E.isogeny_class()
Elliptic curves in class 106722dh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 106722.ct2 | 106722dh1 | \([1, -1, 0, -774846, 271645380]\) | \(-338608873/13552\) | \(-2059089729230307312\) | \([2]\) | \(2211840\) | \(2.2823\) | \(\Gamma_0(N)\)-optimal |
| 106722.ct1 | 106722dh2 | \([1, -1, 0, -12514266, 17042580792]\) | \(1426487591593/2156\) | \(327582456923003436\) | \([2]\) | \(4423680\) | \(2.6289\) |
Rank
sage: E.rank()
The elliptic curves in class 106722dh have rank \(0\).
Complex multiplication
The elliptic curves in class 106722dh do not have complex multiplication.Modular form 106722.2.a.dh
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 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.
