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SageMath
E = EllipticCurve("gb1")
E.isogeny_class()
Elliptic curves in class 109200gb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 109200.fy3 | 109200gb1 | \([0, 1, 0, 5392, -1447212]\) | \(270840023/14329224\) | \(-917070336000000\) | \([]\) | \(559872\) | \(1.5507\) | \(\Gamma_0(N)\)-optimal |
| 109200.fy2 | 109200gb2 | \([0, 1, 0, -48608, 39484788]\) | \(-198461344537/10417365504\) | \(-666711392256000000\) | \([]\) | \(1679616\) | \(2.1000\) | |
| 109200.fy1 | 109200gb3 | \([0, 1, 0, -10422608, 12948016788]\) | \(-1956469094246217097/36641439744\) | \(-2345052143616000000\) | \([]\) | \(5038848\) | \(2.6493\) |
Rank
sage: E.rank()
The elliptic curves in class 109200gb have rank \(0\).
Complex multiplication
The elliptic curves in class 109200gb do not have complex multiplication.Modular form 109200.2.a.gb
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
