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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 9792p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9792.bg2 | 9792p1 | \([0, 0, 0, -147180, -21725008]\) | \(1845026709625/793152\) | \(151573707620352\) | \([2]\) | \(36864\) | \(1.6811\) | \(\Gamma_0(N)\)-optimal |
| 9792.bg3 | 9792p2 | \([0, 0, 0, -124140, -28756816]\) | \(-1107111813625/1228691592\) | \(-234806619817377792\) | \([2]\) | \(73728\) | \(2.0277\) | |
| 9792.bg1 | 9792p3 | \([0, 0, 0, -432300, 82711856]\) | \(46753267515625/11591221248\) | \(2215116875967234048\) | \([2]\) | \(110592\) | \(2.2305\) | |
| 9792.bg4 | 9792p4 | \([0, 0, 0, 1042260, 524490032]\) | \(655215969476375/1001033261568\) | \(-191300435360631226368\) | \([2]\) | \(221184\) | \(2.5770\) |
Rank
sage: E.rank()
The elliptic curves in class 9792p have rank \(1\).
Complex multiplication
The elliptic curves in class 9792p do not have complex multiplication.Modular form 9792.2.a.p
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
