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SageMath
E = EllipticCurve("cx1")
E.isogeny_class()
Elliptic curves in class 335730.cx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 335730.cx1 | 335730cx4 | \([1, 0, 0, -2392896, -1424908440]\) | \(32208729120020809/658986840\) | \(31002616455206040\) | \([2]\) | \(7962624\) | \(2.2839\) | |
| 335730.cx2 | 335730cx2 | \([1, 0, 0, -154696, -20661760]\) | \(8702409880009/1120910400\) | \(52734217290062400\) | \([2, 2]\) | \(3981312\) | \(1.9374\) | |
| 335730.cx3 | 335730cx1 | \([1, 0, 0, -39176, 2650176]\) | \(141339344329/17141760\) | \(806449201090560\) | \([2]\) | \(1990656\) | \(1.5908\) | \(\Gamma_0(N)\)-optimal |
| 335730.cx4 | 335730cx3 | \([1, 0, 0, 235184, -107916904]\) | \(30579142915511/124675335000\) | \(-5865460974045135000\) | \([2]\) | \(7962624\) | \(2.2839\) |
Rank
sage: E.rank()
The elliptic curves in class 335730.cx have rank \(1\).
Complex multiplication
The elliptic curves in class 335730.cx do not have complex multiplication.Modular form 335730.2.a.cx
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.
