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SageMath
E = EllipticCurve("cx1")
E.isogeny_class()
Elliptic curves in class 353600cx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 353600.cx2 | 353600cx1 | \([0, 0, 0, -1172300, -487750000]\) | \(43499078731809/82055753\) | \(336100364288000000\) | \([2]\) | \(4915200\) | \(2.2530\) | \(\Gamma_0(N)\)-optimal |
| 353600.cx1 | 353600cx2 | \([0, 0, 0, -18748300, -31245750000]\) | \(177930109857804849/634933\) | \(2600685568000000\) | \([2]\) | \(9830400\) | \(2.5996\) |
Rank
sage: E.rank()
The elliptic curves in class 353600cx have rank \(0\).
Complex multiplication
The elliptic curves in class 353600cx do not have complex multiplication.Modular form 353600.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
