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SageMath
E = EllipticCurve("ma1")
E.isogeny_class()
Elliptic curves in class 221760.ma
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 221760.ma1 | 221760iv4 | \([0, 0, 0, -11924652, 4490491696]\) | \(981281029968144361/522287841796875\) | \(99810760896000000000000\) | \([2]\) | \(18874368\) | \(3.1045\) | |
| 221760.ma2 | 221760iv2 | \([0, 0, 0, -9358572, 11007308464]\) | \(474334834335054841/607815140625\) | \(116155282231296000000\) | \([2, 2]\) | \(9437184\) | \(2.7579\) | |
| 221760.ma3 | 221760iv1 | \([0, 0, 0, -9355692, 11014428976]\) | \(473897054735271721/779625\) | \(148988657664000\) | \([2]\) | \(4718592\) | \(2.4114\) | \(\Gamma_0(N)\)-optimal |
| 221760.ma4 | 221760iv3 | \([0, 0, 0, -6838572, 17068412464]\) | \(-185077034913624841/551466161890875\) | \(-105386824700643999744000\) | \([2]\) | \(18874368\) | \(3.1045\) |
Rank
sage: E.rank()
The elliptic curves in class 221760.ma have rank \(0\).
Complex multiplication
The elliptic curves in class 221760.ma do not have complex multiplication.Modular form 221760.2.a.ma
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.
