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SageMath
E = EllipticCurve("ps1")
E.isogeny_class()
Elliptic curves in class 705600.ps
sage: E.isogeny_class().curves
| LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
|---|---|---|---|---|---|---|
| 705600.ps1 | \([0, 0, 0, -1896300, 1005102000]\) | \(-5154200289/20\) | \(-2926264320000000\) | \([]\) | \(7741440\) | \(2.1809\) |
| 705600.ps2 | \([0, 0, 0, 13223700, -9536562000]\) | \(1747829720511/1280000000\) | \(-187280916480000000000000\) | \([]\) | \(54190080\) | \(3.1539\) |
Rank
sage: E.rank()
The elliptic curves in class 705600.ps have rank \(1\).
Complex multiplication
The elliptic curves in class 705600.ps do not have complex multiplication.Modular form 705600.2.a.ps
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
