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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 80064bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 80064.bn1 | 80064bd1 | \([0, 0, 0, -44940, -3666832]\) | \(210094874500/3753\) | \(179302367232\) | \([2]\) | \(172032\) | \(1.2864\) | \(\Gamma_0(N)\)-optimal |
| 80064.bn2 | 80064bd2 | \([0, 0, 0, -43500, -3912784]\) | \(-95269531250/14085009\) | \(-1345843568443392\) | \([2]\) | \(344064\) | \(1.6330\) |
Rank
sage: E.rank()
The elliptic curves in class 80064bd have rank \(1\).
Complex multiplication
The elliptic curves in class 80064bd do not have complex multiplication.Modular form 80064.2.a.bd
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.
