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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 29645h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 29645.c4 | 29645h1 | \([1, -1, 1, 4817, 98662]\) | \(59319/55\) | \(-11463230904895\) | \([2]\) | \(46080\) | \(1.1931\) | \(\Gamma_0(N)\)-optimal |
| 29645.c3 | 29645h2 | \([1, -1, 1, -24828, 905006]\) | \(8120601/3025\) | \(630477699769225\) | \([2, 2]\) | \(92160\) | \(1.5397\) | |
| 29645.c2 | 29645h3 | \([1, -1, 1, -173053, -27020584]\) | \(2749884201/73205\) | \(15257560334415245\) | \([2]\) | \(184320\) | \(1.8862\) | |
| 29645.c1 | 29645h4 | \([1, -1, 1, -350923, 80080872]\) | \(22930509321/6875\) | \(1432903863111875\) | \([2]\) | \(184320\) | \(1.8862\) |
Rank
sage: E.rank()
The elliptic curves in class 29645h have rank \(1\).
Complex multiplication
The elliptic curves in class 29645h do not have complex multiplication.Modular form 29645.2.a.h
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
