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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 154721.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 154721.a1 | 154721a4 | \([1, -1, 1, -118864, -15739964]\) | \(209267191953/55223\) | \(49010615775863\) | \([2]\) | \(604800\) | \(1.6114\) | |
| 154721.a2 | 154721a2 | \([1, -1, 1, -8349, -179452]\) | \(72511713/25921\) | \(23004982915201\) | \([2, 2]\) | \(302400\) | \(1.2648\) | |
| 154721.a3 | 154721a1 | \([1, -1, 1, -3544, 80018]\) | \(5545233/161\) | \(142888092641\) | \([2]\) | \(151200\) | \(0.91821\) | \(\Gamma_0(N)\)-optimal |
| 154721.a4 | 154721a3 | \([1, -1, 1, 25286, -1282680]\) | \(2014698447/1958887\) | \(-1738519423163047\) | \([2]\) | \(604800\) | \(1.6114\) |
Rank
sage: E.rank()
The elliptic curves in class 154721.a have rank \(0\).
Complex multiplication
The elliptic curves in class 154721.a do not have complex multiplication.Modular form 154721.2.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.
