Show commands:
SageMath
E = EllipticCurve("ce1")
E.isogeny_class()
Elliptic curves in class 72128ce
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 72128.g1 | 72128ce1 | \([0, 1, 0, -8689, -251889]\) | \(109744/23\) | \(15206530433024\) | \([2]\) | \(172032\) | \(1.2442\) | \(\Gamma_0(N)\)-optimal |
| 72128.g2 | 72128ce2 | \([0, 1, 0, 18751, -1497665]\) | \(275684/529\) | \(-1399000799838208\) | \([2]\) | \(344064\) | \(1.5908\) |
Rank
sage: E.rank()
The elliptic curves in class 72128ce have rank \(0\).
Complex multiplication
The elliptic curves in class 72128ce do not have complex multiplication.Modular form 72128.2.a.ce
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.
