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SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 9360.bz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9360.bz1 | 9360bh4 | \([0, 0, 0, -72387, -4490046]\) | \(520300455507/193072360\) | \(15565796400660480\) | \([2]\) | \(82944\) | \(1.8070\) | |
| 9360.bz2 | 9360bh2 | \([0, 0, 0, -63987, -6229966]\) | \(261984288445803/42250\) | \(4672512000\) | \([2]\) | \(27648\) | \(1.2576\) | |
| 9360.bz3 | 9360bh1 | \([0, 0, 0, -3987, -97966]\) | \(-63378025803/812500\) | \(-89856000000\) | \([2]\) | \(13824\) | \(0.91107\) | \(\Gamma_0(N)\)-optimal |
| 9360.bz4 | 9360bh3 | \([0, 0, 0, 14013, -498366]\) | \(3774555693/3515200\) | \(-283400935833600\) | \([2]\) | \(41472\) | \(1.4604\) |
Rank
sage: E.rank()
The elliptic curves in class 9360.bz have rank \(0\).
Complex multiplication
The elliptic curves in class 9360.bz do not have complex multiplication.Modular form 9360.2.a.bz
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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
