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SageMath
E = EllipticCurve("dt1")
E.isogeny_class()
Elliptic curves in class 19600dt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 19600.cz3 | 19600dt1 | \([0, 1, 0, -408, -37612]\) | \(-25/2\) | \(-602362880000\) | \([]\) | \(17280\) | \(0.94000\) | \(\Gamma_0(N)\)-optimal |
| 19600.cz1 | 19600dt2 | \([0, 1, 0, -98408, -11915212]\) | \(-349938025/8\) | \(-2409451520000\) | \([]\) | \(51840\) | \(1.4893\) | |
| 19600.cz2 | 19600dt3 | \([0, 1, 0, -59208, 6665588]\) | \(-121945/32\) | \(-6023628800000000\) | \([]\) | \(86400\) | \(1.7447\) | |
| 19600.cz4 | 19600dt4 | \([0, 1, 0, 430792, -49194412]\) | \(46969655/32768\) | \(-6168195891200000000\) | \([]\) | \(259200\) | \(2.2940\) |
Rank
sage: E.rank()
The elliptic curves in class 19600dt have rank \(0\).
Complex multiplication
The elliptic curves in class 19600dt do not have complex multiplication.Modular form 19600.2.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.
\(\left(\begin{array}{rrrr} 1 & 3 & 5 & 15 \\ 3 & 1 & 15 & 5 \\ 5 & 15 & 1 & 3 \\ 15 & 5 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
