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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 244398bi
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 244398.bi3 | 244398bi1 | \([1, 0, 0, -69839, -6563847]\) | \(254478514753/21762048\) | \(3221564122140672\) | \([2]\) | \(1824768\) | \(1.7169\) | \(\Gamma_0(N)\)-optimal |
| 244398.bi2 | 244398bi2 | \([1, 0, 0, -239119, 37482809]\) | \(10214075575873/1806590016\) | \(267440159077084224\) | \([2, 2]\) | \(3649536\) | \(2.0635\) | |
| 244398.bi1 | 244398bi3 | \([1, 0, 0, -3645879, 2679084513]\) | \(36204575259448513/1527466248\) | \(226119823940174472\) | \([2]\) | \(7299072\) | \(2.4101\) | |
| 244398.bi4 | 244398bi4 | \([1, 0, 0, 459161, 215544209]\) | \(72318867421247/177381135624\) | \(-26258774103928409736\) | \([2]\) | \(7299072\) | \(2.4101\) |
Rank
sage: E.rank()
The elliptic curves in class 244398bi have rank \(0\).
Complex multiplication
The elliptic curves in class 244398bi do not have complex multiplication.Modular form 244398.2.a.bi
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
