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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 9360bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9360.l4 | 9360bl1 | \([0, 0, 0, -963, -4158]\) | \(33076161/16640\) | \(49686773760\) | \([2]\) | \(6144\) | \(0.74509\) | \(\Gamma_0(N)\)-optimal |
| 9360.l2 | 9360bl2 | \([0, 0, 0, -12483, -536382]\) | \(72043225281/67600\) | \(201852518400\) | \([2, 2]\) | \(12288\) | \(1.0917\) | |
| 9360.l1 | 9360bl3 | \([0, 0, 0, -199683, -34344702]\) | \(294889639316481/260\) | \(776355840\) | \([2]\) | \(24576\) | \(1.4382\) | |
| 9360.l3 | 9360bl4 | \([0, 0, 0, -9603, -790398]\) | \(-32798729601/71402500\) | \(-213206722560000\) | \([2]\) | \(24576\) | \(1.4382\) |
Rank
sage: E.rank()
The elliptic curves in class 9360bl have rank \(0\).
Complex multiplication
The elliptic curves in class 9360bl do not have complex multiplication.Modular form 9360.2.a.bl
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.
