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SageMath
E = EllipticCurve("ep1")
E.isogeny_class()
Elliptic curves in class 154560.ep
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 154560.ep1 | 154560by1 | \([0, 1, 0, -14721, 585855]\) | \(1345938541921/203765625\) | \(53415936000000\) | \([2]\) | \(393216\) | \(1.3581\) | \(\Gamma_0(N)\)-optimal |
| 154560.ep2 | 154560by2 | \([0, 1, 0, 25279, 3249855]\) | \(6814692748079/21258460125\) | \(-5572777771008000\) | \([2]\) | \(786432\) | \(1.7046\) |
Rank
sage: E.rank()
The elliptic curves in class 154560.ep have rank \(1\).
Complex multiplication
The elliptic curves in class 154560.ep do not have complex multiplication.Modular form 154560.2.a.ep
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.
