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SageMath
E = EllipticCurve("dg1")
E.isogeny_class()
Elliptic curves in class 159120dg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 159120.du3 | 159120dg1 | \([0, 0, 0, -7842, 224651]\) | \(4572531595264/776953125\) | \(9062381250000\) | \([2]\) | \(294912\) | \(1.2069\) | \(\Gamma_0(N)\)-optimal |
| 159120.du2 | 159120dg2 | \([0, 0, 0, -35967, -2413474]\) | \(27572037674704/2472575625\) | \(461441953440000\) | \([2, 2]\) | \(589824\) | \(1.5535\) | |
| 159120.du4 | 159120dg3 | \([0, 0, 0, 40533, -11302774]\) | \(9865576607324/79640206425\) | \(-59451095535436800\) | \([2]\) | \(1179648\) | \(1.9001\) | |
| 159120.du1 | 159120dg4 | \([0, 0, 0, -562467, -162364174]\) | \(26362547147244676/244298925\) | \(182368170316800\) | \([2]\) | \(1179648\) | \(1.9001\) |
Rank
sage: E.rank()
The elliptic curves in class 159120dg have rank \(0\).
Complex multiplication
The elliptic curves in class 159120dg do not have complex multiplication.Modular form 159120.2.a.dg
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.
