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SageMath
E = EllipticCurve("ia1")
E.isogeny_class()
Elliptic curves in class 286650.ia
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 286650.ia1 | 286650ia2 | \([1, -1, 0, -1553652, 743403856]\) | \(38686490446661/141927552\) | \(1521571949758224000\) | \([2]\) | \(8257536\) | \(2.3493\) | |
| 286650.ia2 | 286650ia1 | \([1, -1, 0, -142452, -298544]\) | \(29819839301/17252352\) | \(184958413645824000\) | \([2]\) | \(4128768\) | \(2.0027\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 286650.ia have rank \(0\).
Complex multiplication
The elliptic curves in class 286650.ia do not have complex multiplication.Modular form 286650.2.a.ia
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
