Show commands:
SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 457776a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 457776.a1 | 457776a1 | \([0, 0, 0, -1239741507, 16659764322370]\) | \(595099203230897/5780865024\) | \(2047012986782529486587953152\) | \([2]\) | \(561512448\) | \(4.0601\) | \(\Gamma_0(N)\)-optimal |
| 457776.a2 | 457776a2 | \([0, 0, 0, -334177347, 40475196166210]\) | \(-11655394135217/1991891886336\) | \(-705331908402734935478268592128\) | \([2]\) | \(1123024896\) | \(4.4067\) |
Rank
sage: E.rank()
The elliptic curves in class 457776a have rank \(1\).
Complex multiplication
The elliptic curves in class 457776a do not have complex multiplication.Modular form 457776.2.a.a
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.
