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SageMath
E = EllipticCurve("il1")
E.isogeny_class()
Elliptic curves in class 221760il
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 221760.la4 | 221760il1 | \([0, 0, 0, 5748, -1370896]\) | \(109902239/4312000\) | \(-824036032512000\) | \([2]\) | \(884736\) | \(1.5420\) | \(\Gamma_0(N)\)-optimal |
| 221760.la2 | 221760il2 | \([0, 0, 0, -155532, -22595344]\) | \(2177286259681/105875000\) | \(20233027584000000\) | \([2]\) | \(1769472\) | \(1.8885\) | |
| 221760.la3 | 221760il3 | \([0, 0, 0, -51852, 37497584]\) | \(-80677568161/3131816380\) | \(-598499430503546880\) | \([2]\) | \(2654208\) | \(2.0913\) | |
| 221760.la1 | 221760il4 | \([0, 0, 0, -2027532, 1105155056]\) | \(4823468134087681/30382271150\) | \(5806142434403942400\) | \([2]\) | \(5308416\) | \(2.4378\) |
Rank
sage: E.rank()
The elliptic curves in class 221760il have rank \(0\).
Complex multiplication
The elliptic curves in class 221760il do not have complex multiplication.Modular form 221760.2.a.il
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
