Show commands:
SageMath
E = EllipticCurve("cl1")
E.isogeny_class()
Elliptic curves in class 46200.cl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 46200.cl1 | 46200bh6 | \([0, 1, 0, -51334008, -141582106512]\) | \(467508233804095622882/315748125\) | \(10103940000000000\) | \([2]\) | \(2359296\) | \(2.8208\) | |
| 46200.cl2 | 46200bh4 | \([0, 1, 0, -3209008, -2212106512]\) | \(228410605013945764/187597265625\) | \(3001556250000000000\) | \([2, 2]\) | \(1179648\) | \(2.4742\) | |
| 46200.cl3 | 46200bh5 | \([0, 1, 0, -2516008, -3193394512]\) | \(-55043996611705922/105743408203125\) | \(-3383789062500000000000\) | \([2]\) | \(2359296\) | \(2.8208\) | |
| 46200.cl4 | 46200bh3 | \([0, 1, 0, -2082008, 1142923488]\) | \(62380825826921284/787768887675\) | \(12604302202800000000\) | \([2]\) | \(1179648\) | \(2.4742\) | |
| 46200.cl5 | 46200bh2 | \([0, 1, 0, -244508, -18376512]\) | \(404151985581136/197735855625\) | \(790943422500000000\) | \([2, 2]\) | \(589824\) | \(2.1277\) | |
| 46200.cl6 | 46200bh1 | \([0, 1, 0, 55617, -2169762]\) | \(76102438406144/52315569075\) | \(-13078892268750000\) | \([2]\) | \(294912\) | \(1.7811\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 46200.cl have rank \(1\).
Complex multiplication
The elliptic curves in class 46200.cl do not have complex multiplication.Modular form 46200.2.a.cl
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
