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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 14490bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 14490.bg4 | 14490bl1 | \([1, -1, 1, -30682418, 57042898481]\) | \(4381924769947287308715481/608122186185572352000\) | \(443321073729282244608000\) | \([2]\) | \(2580480\) | \(3.2639\) | \(\Gamma_0(N)\)-optimal |
| 14490.bg2 | 14490bl2 | \([1, -1, 1, -473234738, 3962478612017]\) | \(16077778198622525072705635801/388799208512064000000\) | \(283434623005294656000000\) | \([2, 2]\) | \(5160960\) | \(3.6105\) | |
| 14490.bg1 | 14490bl3 | \([1, -1, 1, -7571711858, 253596043186481]\) | \(65853432878493908038433301506521/38511703125000000\) | \(28075031578125000000\) | \([2]\) | \(10321920\) | \(3.9570\) | |
| 14490.bg3 | 14490bl4 | \([1, -1, 1, -455594738, 4271489076017]\) | \(-14346048055032350809895395801/2509530875136386550792000\) | \(-1829448007974425795527368000\) | \([2]\) | \(10321920\) | \(3.9570\) |
Rank
sage: E.rank()
The elliptic curves in class 14490bl have rank \(1\).
Complex multiplication
The elliptic curves in class 14490bl do not have complex multiplication.Modular form 14490.2.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 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.
