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SageMath
E = EllipticCurve("do1")
E.isogeny_class()
Elliptic curves in class 40656.do
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 40656.do1 | 40656cu2 | \([0, 1, 0, -4396, -113368]\) | \(20720464/63\) | \(28571735808\) | \([2]\) | \(67200\) | \(0.87496\) | |
| 40656.do2 | 40656cu1 | \([0, 1, 0, -161, -3258]\) | \(-16384/147\) | \(-4166711472\) | \([2]\) | \(33600\) | \(0.52839\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 40656.do have rank \(0\).
Complex multiplication
The elliptic curves in class 40656.do do not have complex multiplication.Modular form 40656.2.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.
