Show commands:
SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 38720q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38720.da4 | 38720q1 | \([0, -1, 0, -21941, -1217995]\) | \(643956736/15125\) | \(27437936768000\) | \([2]\) | \(138240\) | \(1.3641\) | \(\Gamma_0(N)\)-optimal |
| 38720.da3 | 38720q2 | \([0, -1, 0, -48561, 2343761]\) | \(436334416/171875\) | \(4988715776000000\) | \([2]\) | \(276480\) | \(1.7107\) | |
| 38720.da2 | 38720q3 | \([0, -1, 0, -215541, 38102165]\) | \(610462990336/8857805\) | \(16068753288811520\) | \([2]\) | \(414720\) | \(1.9134\) | |
| 38720.da1 | 38720q4 | \([0, -1, 0, -3436561, 2453222961]\) | \(154639330142416/33275\) | \(965815374233600\) | \([2]\) | \(829440\) | \(2.2600\) |
Rank
sage: E.rank()
The elliptic curves in class 38720q have rank \(0\).
Complex multiplication
The elliptic curves in class 38720q do not have complex multiplication.Modular form 38720.2.a.q
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.
