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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 25350bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 25350.bn4 | 25350bq1 | \([1, 0, 1, -511, -6082]\) | \(-24389/12\) | \(-7240213500\) | \([2]\) | \(15360\) | \(0.59720\) | \(\Gamma_0(N)\)-optimal |
| 25350.bn2 | 25350bq2 | \([1, 0, 1, -8961, -327182]\) | \(131872229/18\) | \(10860320250\) | \([2]\) | \(30720\) | \(0.94378\) | |
| 25350.bn3 | 25350bq3 | \([1, 0, 1, -4736, 602318]\) | \(-19465109/248832\) | \(-150133067136000\) | \([2]\) | \(76800\) | \(1.4019\) | |
| 25350.bn1 | 25350bq4 | \([1, 0, 1, -139936, 20071118]\) | \(502270291349/1889568\) | \(1140072978564000\) | \([2]\) | \(153600\) | \(1.7485\) |
Rank
sage: E.rank()
The elliptic curves in class 25350bq have rank \(1\).
Complex multiplication
The elliptic curves in class 25350bq do not have complex multiplication.Modular form 25350.2.a.bq
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
