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SageMath
E = EllipticCurve("gu1")
E.isogeny_class()
Elliptic curves in class 103488gu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 103488.g3 | 103488gu1 | \([0, -1, 0, -141185, 14930721]\) | \(10091699281/2737152\) | \(84416448599949312\) | \([2]\) | \(1382400\) | \(1.9558\) | \(\Gamma_0(N)\)-optimal |
| 103488.g4 | 103488gu2 | \([0, -1, 0, 360575, 96717601]\) | \(168105213359/228637728\) | \(-7051411472114515968\) | \([2]\) | \(2764800\) | \(2.3024\) | |
| 103488.g1 | 103488gu3 | \([0, -1, 0, -31563905, -68244436959]\) | \(112763292123580561/1932612\) | \(59603646988419072\) | \([2]\) | \(6912000\) | \(2.7605\) | |
| 103488.g2 | 103488gu4 | \([0, -1, 0, -31532545, -68386842719]\) | \(-112427521449300721/466873642818\) | \(-14398840426697819947008\) | \([2]\) | \(13824000\) | \(3.1071\) |
Rank
sage: E.rank()
The elliptic curves in class 103488gu have rank \(0\).
Complex multiplication
The elliptic curves in class 103488gu do not have complex multiplication.Modular form 103488.2.a.gu
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
