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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 154560bo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 154560.fz4 | 154560bo1 | \([0, 1, 0, -218186081, 1081484185119]\) | \(4381924769947287308715481/608122186185572352000\) | \(159415582375430678642688000\) | \([2]\) | \(61931520\) | \(3.7543\) | \(\Gamma_0(N)\)-optimal |
| 154560.fz2 | 154560bo2 | \([0, 1, 0, -3365224801, 75136969936415]\) | \(16077778198622525072705635801/388799208512064000000\) | \(101921379716186505216000000\) | \([2, 2]\) | \(123863040\) | \(4.1009\) | |
| 154560.fz1 | 154560bo3 | \([0, 1, 0, -53843284321, 4808878531214879]\) | \(65853432878493908038433301506521/38511703125000000\) | \(10095611904000000000000\) | \([2]\) | \(247726080\) | \(4.4474\) | |
| 154560.fz3 | 154560bo4 | \([0, 1, 0, -3239784801, 80996849360415]\) | \(-14346048055032350809895395801/2509530875136386550792000\) | \(-657858461731752915970818048000\) | \([2]\) | \(247726080\) | \(4.4474\) |
Rank
sage: E.rank()
The elliptic curves in class 154560bo have rank \(0\).
Complex multiplication
The elliptic curves in class 154560bo do not have complex multiplication.Modular form 154560.2.a.bo
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
