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SageMath
E = EllipticCurve("dr1")
E.isogeny_class()
Elliptic curves in class 10800.dr
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10800.dr1 | 10800dt2 | \([0, 0, 0, -7275, -226150]\) | \(68450475/4096\) | \(2548039680000\) | \([]\) | \(20736\) | \(1.1333\) | |
| 10800.dr2 | 10800dt1 | \([0, 0, 0, -1275, 17450]\) | \(3316275/16\) | \(1105920000\) | \([]\) | \(6912\) | \(0.58397\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 10800.dr have rank \(0\).
Complex multiplication
The elliptic curves in class 10800.dr do not have complex multiplication.Modular form 10800.2.a.dr
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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
