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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 100800.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 100800.u1 | 100800md4 | \([0, 0, 0, -1562700, 707866000]\) | \(282678688658/18600435\) | \(27770300651520000000\) | \([2]\) | \(2359296\) | \(2.4805\) | |
| 100800.u2 | 100800md2 | \([0, 0, 0, -302700, -50654000]\) | \(4108974916/893025\) | \(666639590400000000\) | \([2, 2]\) | \(1179648\) | \(2.1339\) | |
| 100800.u3 | 100800md1 | \([0, 0, 0, -284700, -58466000]\) | \(13674725584/945\) | \(176359680000000\) | \([2]\) | \(589824\) | \(1.7874\) | \(\Gamma_0(N)\)-optimal |
| 100800.u4 | 100800md3 | \([0, 0, 0, 669300, -309206000]\) | \(22208984782/40516875\) | \(-60491370240000000000\) | \([2]\) | \(2359296\) | \(2.4805\) |
Rank
sage: E.rank()
The elliptic curves in class 100800.u have rank \(1\).
Complex multiplication
The elliptic curves in class 100800.u do not have complex multiplication.Modular form 100800.2.a.u
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.
