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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 9360.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9360.z1 | 9360br3 | \([0, 0, 0, -29883, -1908502]\) | \(988345570681/44994560\) | \(134353036247040\) | \([2]\) | \(41472\) | \(1.4729\) | |
| 9360.z2 | 9360br1 | \([0, 0, 0, -4683, 122618]\) | \(3803721481/26000\) | \(77635584000\) | \([2]\) | \(13824\) | \(0.92360\) | \(\Gamma_0(N)\)-optimal |
| 9360.z3 | 9360br2 | \([0, 0, 0, -1803, 271802]\) | \(-217081801/10562500\) | \(-31539456000000\) | \([2]\) | \(27648\) | \(1.2702\) | |
| 9360.z4 | 9360br4 | \([0, 0, 0, 16197, -7262998]\) | \(157376536199/7722894400\) | \(-23060439112089600\) | \([2]\) | \(82944\) | \(1.8195\) |
Rank
sage: E.rank()
The elliptic curves in class 9360.z have rank \(0\).
Complex multiplication
The elliptic curves in class 9360.z do not have complex multiplication.Modular form 9360.2.a.z
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.
