Show commands:
SageMath
E = EllipticCurve("cs1")
E.isogeny_class()
Elliptic curves in class 29400.cs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 29400.cs1 | 29400bu4 | \([0, 1, 0, -3548008, -2573228512]\) | \(2624033547076/324135\) | \(610146537840000000\) | \([2]\) | \(884736\) | \(2.4360\) | |
| 29400.cs2 | 29400bu2 | \([0, 1, 0, -240508, -33068512]\) | \(3269383504/893025\) | \(420253992900000000\) | \([2, 2]\) | \(442368\) | \(2.0894\) | |
| 29400.cs3 | 29400bu1 | \([0, 1, 0, -87383, 9500238]\) | \(2508888064/118125\) | \(3474322031250000\) | \([2]\) | \(221184\) | \(1.7428\) | \(\Gamma_0(N)\)-optimal |
| 29400.cs4 | 29400bu3 | \([0, 1, 0, 616992, -214858512]\) | \(13799183324/18600435\) | \(-35013161237040000000\) | \([2]\) | \(884736\) | \(2.4360\) |
Rank
sage: E.rank()
The elliptic curves in class 29400.cs have rank \(1\).
Complex multiplication
The elliptic curves in class 29400.cs do not have complex multiplication.Modular form 29400.2.a.cs
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.
