Show commands:
SageMath
E = EllipticCurve("di1")
E.isogeny_class()
Elliptic curves in class 266560di
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 266560.di3 | 266560di1 | \([0, 0, 0, -28028, 1805552]\) | \(1263257424/425\) | \(819213516800\) | \([2]\) | \(393216\) | \(1.2582\) | \(\Gamma_0(N)\)-optimal |
| 266560.di2 | 266560di2 | \([0, 0, 0, -31948, 1267728]\) | \(467720676/180625\) | \(1392662978560000\) | \([2, 2]\) | \(786432\) | \(1.6048\) | |
| 266560.di4 | 266560di3 | \([0, 0, 0, 101332, 9104592]\) | \(7462174302/6640625\) | \(-102401689600000000\) | \([2]\) | \(1572864\) | \(1.9514\) | |
| 266560.di1 | 266560di4 | \([0, 0, 0, -227948, -40989872]\) | \(84944038338/2088025\) | \(32198368064307200\) | \([2]\) | \(1572864\) | \(1.9514\) |
Rank
sage: E.rank()
The elliptic curves in class 266560di have rank \(1\).
Complex multiplication
The elliptic curves in class 266560di do not have complex multiplication.Modular form 266560.2.a.di
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.
