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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 9360.bm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9360.bm1 | 9360q3 | \([0, 0, 0, -89067, -4870726]\) | \(52337949619538/23423590125\) | \(34971232667904000\) | \([2]\) | \(49152\) | \(1.8699\) | |
| 9360.bm2 | 9360q2 | \([0, 0, 0, -44067, 3508274]\) | \(12677589459076/213890625\) | \(159668496000000\) | \([2, 2]\) | \(24576\) | \(1.5233\) | |
| 9360.bm3 | 9360q1 | \([0, 0, 0, -43887, 3538766]\) | \(50091484483024/14625\) | \(2729376000\) | \([2]\) | \(12288\) | \(1.1767\) | \(\Gamma_0(N)\)-optimal |
| 9360.bm4 | 9360q4 | \([0, 0, 0, -1947, 9935786]\) | \(-546718898/28564453125\) | \(-42646500000000000\) | \([2]\) | \(49152\) | \(1.8699\) |
Rank
sage: E.rank()
The elliptic curves in class 9360.bm have rank \(1\).
Complex multiplication
The elliptic curves in class 9360.bm do not have complex multiplication.Modular form 9360.2.a.bm
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
