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SageMath
E = EllipticCurve("dt1")
E.isogeny_class()
Elliptic curves in class 112896dt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 112896.dj3 | 112896dt1 | \([0, 0, 0, -3234, -68600]\) | \(85184/3\) | \(131736761856\) | \([2]\) | \(92160\) | \(0.90455\) | \(\Gamma_0(N)\)-optimal |
| 112896.dj4 | 112896dt2 | \([0, 0, 0, 1176, -241472]\) | \(64/9\) | \(-25293458276352\) | \([2]\) | \(184320\) | \(1.2511\) | |
| 112896.dj1 | 112896dt3 | \([0, 0, 0, -285474, 58707880]\) | \(58591911104/243\) | \(10670677710336\) | \([2]\) | \(460800\) | \(1.7093\) | |
| 112896.dj2 | 112896dt4 | \([0, 0, 0, -281064, 60609472]\) | \(-873722816/59049\) | \(-165950379751145472\) | \([2]\) | \(921600\) | \(2.0558\) |
Rank
sage: E.rank()
The elliptic curves in class 112896dt have rank \(0\).
Complex multiplication
The elliptic curves in class 112896dt do not have complex multiplication.Modular form 112896.2.a.dt
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
