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SageMath
E = EllipticCurve("do1")
E.isogeny_class()
Elliptic curves in class 372645do
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 372645.do2 | 372645do1 | \([1, -1, 0, -10425, -391000]\) | \(2803221/125\) | \(5587634768625\) | \([2]\) | \(737280\) | \(1.2086\) | \(\Gamma_0(N)\)-optimal |
| 372645.do1 | 372645do2 | \([1, -1, 0, -28170, 1308971]\) | \(55306341/15625\) | \(698454346078125\) | \([2]\) | \(1474560\) | \(1.5552\) |
Rank
sage: E.rank()
The elliptic curves in class 372645do have rank \(2\).
Complex multiplication
The elliptic curves in class 372645do do not have complex multiplication.Modular form 372645.2.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 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.
