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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 9360bo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9360.g4 | 9360bo1 | \([0, 0, 0, 575637, 6333338]\) | \(7064514799444439/4094064000000\) | \(-12224809598976000000\) | \([2]\) | \(138240\) | \(2.3520\) | \(\Gamma_0(N)\)-optimal |
| 9360.g3 | 9360bo2 | \([0, 0, 0, -2304363, 50685338]\) | \(453198971846635561/261896250564000\) | \(782018013844094976000\) | \([2]\) | \(276480\) | \(2.6985\) | |
| 9360.g2 | 9360bo3 | \([0, 0, 0, -7686363, -8847711862]\) | \(-16818951115904497561/1592332281446400\) | \(-4754678715082447257600\) | \([2]\) | \(414720\) | \(2.9013\) | |
| 9360.g1 | 9360bo4 | \([0, 0, 0, -125651163, -542119386742]\) | \(73474353581350183614361/576510977802240\) | \(1721452555541843804160\) | \([2]\) | \(829440\) | \(3.2478\) |
Rank
sage: E.rank()
The elliptic curves in class 9360bo have rank \(0\).
Complex multiplication
The elliptic curves in class 9360bo do not have complex multiplication.Modular form 9360.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
