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SageMath
E = EllipticCurve("du1")
E.isogeny_class()
Elliptic curves in class 54720.du
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 54720.du1 | 54720bm4 | \([0, 0, 0, -1094412, -440675984]\) | \(3034301922374404/1425\) | \(68080435200\) | \([2]\) | \(262144\) | \(1.8523\) | |
| 54720.du2 | 54720bm3 | \([0, 0, 0, -82092, -3933776]\) | \(1280615525284/601171875\) | \(28721433600000000\) | \([2]\) | \(262144\) | \(1.8523\) | |
| 54720.du3 | 54720bm2 | \([0, 0, 0, -68412, -6883184]\) | \(2964647793616/2030625\) | \(24253655040000\) | \([2, 2]\) | \(131072\) | \(1.5058\) | |
| 54720.du4 | 54720bm1 | \([0, 0, 0, -3432, -151256]\) | \(-5988775936/9774075\) | \(-7296307891200\) | \([2]\) | \(65536\) | \(1.1592\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 54720.du have rank \(1\).
Complex multiplication
The elliptic curves in class 54720.du do not have complex multiplication.Modular form 54720.2.a.du
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
