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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 9360bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9360.bu1 | 9360bg1 | \([0, 0, 0, -672, -6736]\) | \(-303464448/1625\) | \(-179712000\) | \([]\) | \(3456\) | \(0.42843\) | \(\Gamma_0(N)\)-optimal |
| 9360.bu2 | 9360bg2 | \([0, 0, 0, 1728, -35856]\) | \(7077888/10985\) | \(-885627924480\) | \([]\) | \(10368\) | \(0.97774\) |
Rank
sage: E.rank()
The elliptic curves in class 9360bg have rank \(0\).
Complex multiplication
The elliptic curves in class 9360bg do not have complex multiplication.Modular form 9360.2.a.bg
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
