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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 81225bi
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 81225.bq2 | 81225bi1 | \([0, 0, 1, 1597425, -887597469]\) | \(841232384/1121931\) | \(-601222614976840921875\) | \([]\) | \(4838400\) | \(2.6729\) | \(\Gamma_0(N)\)-optimal |
| 81225.bq1 | 81225bi2 | \([0, 0, 1, -356604825, -2591969158719]\) | \(-9358714467168256/22284891\) | \(-11942071697362732171875\) | \([]\) | \(24192000\) | \(3.4777\) |
Rank
sage: E.rank()
The elliptic curves in class 81225bi have rank \(1\).
Complex multiplication
The elliptic curves in class 81225bi do not have complex multiplication.Modular form 81225.2.a.bi
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
