Show commands:
SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 203280.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 203280.a1 | 203280gz3 | \([0, -1, 0, -24516576, 45368464176]\) | \(898353183174324196/29899176238575\) | \(54239451705739433548800\) | \([2]\) | \(22118400\) | \(3.1352\) | |
| 203280.a2 | 203280gz2 | \([0, -1, 0, -3765076, -1828747424]\) | \(13015144447800784/4341909875625\) | \(1969141299500057760000\) | \([2, 2]\) | \(11059200\) | \(2.7886\) | |
| 203280.a3 | 203280gz1 | \([0, -1, 0, -3386951, -2397598674]\) | \(151591373397612544/32558203125\) | \(922861486181250000\) | \([2]\) | \(5529600\) | \(2.4420\) | \(\Gamma_0(N)\)-optimal |
| 203280.a4 | 203280gz4 | \([0, -1, 0, 10936424, -12625529024]\) | \(79743193254623804/84085819746075\) | \(-152538274729140606028800\) | \([2]\) | \(22118400\) | \(3.1352\) |
Rank
sage: E.rank()
The elliptic curves in class 203280.a have rank \(0\).
Complex multiplication
The elliptic curves in class 203280.a do not have complex multiplication.Modular form 203280.2.a.a
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
