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SageMath
E = EllipticCurve("dx1")
E.isogeny_class()
Elliptic curves in class 106722dx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 106722.h2 | 106722dx1 | \([1, -1, 0, -1557474, -760380076]\) | \(-2749884201/54208\) | \(-8236358916921229248\) | \([2]\) | \(4423680\) | \(2.4226\) | \(\Gamma_0(N)\)-optimal |
| 106722.h1 | 106722dx2 | \([1, -1, 0, -25036314, -48211115716]\) | \(11422548526761/4312\) | \(655164913846006872\) | \([2]\) | \(8847360\) | \(2.7692\) |
Rank
sage: E.rank()
The elliptic curves in class 106722dx have rank \(0\).
Complex multiplication
The elliptic curves in class 106722dx do not have complex multiplication.Modular form 106722.2.a.dx
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.
