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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 327990.bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 327990.bl1 | 327990bl4 | \([1, 0, 0, -406641, -99824049]\) | \(12501706118329/2570490\) | \(1528987398397290\) | \([2]\) | \(2867200\) | \(1.9107\) | |
| 327990.bl2 | 327990bl2 | \([1, 0, 0, -28191, -1199979]\) | \(4165509529/1368900\) | \(814253644116900\) | \([2, 2]\) | \(1433600\) | \(1.5641\) | |
| 327990.bl3 | 327990bl1 | \([1, 0, 0, -11371, 451745]\) | \(273359449/9360\) | \(5567546284560\) | \([2]\) | \(716800\) | \(1.2175\) | \(\Gamma_0(N)\)-optimal |
| 327990.bl4 | 327990bl3 | \([1, 0, 0, 81139, -8218965]\) | \(99317171591/106616250\) | \(-63417831897566250\) | \([2]\) | \(2867200\) | \(1.9107\) |
Rank
sage: E.rank()
The elliptic curves in class 327990.bl have rank \(1\).
Complex multiplication
The elliptic curves in class 327990.bl do not have complex multiplication.Modular form 327990.2.a.bl
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.
