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SageMath
E = EllipticCurve("do1")
E.isogeny_class()
Elliptic curves in class 107712.do
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 107712.do1 | 107712bk2 | \([0, 0, 0, -1719084, 865334320]\) | \(2940001530995593/8673562656\) | \(1657543636084064256\) | \([2]\) | \(1474560\) | \(2.3660\) | |
| 107712.do2 | 107712bk1 | \([0, 0, 0, -152364, 1131568]\) | \(2046931732873/1181672448\) | \(225821121470005248\) | \([2]\) | \(737280\) | \(2.0194\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 107712.do have rank \(1\).
Complex multiplication
The elliptic curves in class 107712.do do not have complex multiplication.Modular form 107712.2.a.do
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
