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SageMath
E = EllipticCurve("cf1")
E.isogeny_class()
Elliptic curves in class 88218.cf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 88218.cf1 | 88218ce2 | \([1, -1, 1, -692087, 223285443]\) | \(-10418796526321/82044596\) | \(-288693910298765556\) | \([]\) | \(1404000\) | \(2.1789\) | |
| 88218.cf2 | 88218ce1 | \([1, -1, 1, 7573, -423237]\) | \(13651919/29696\) | \(-104492614726656\) | \([]\) | \(280800\) | \(1.3742\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 88218.cf have rank \(0\).
Complex multiplication
The elliptic curves in class 88218.cf do not have complex multiplication.Modular form 88218.2.a.cf
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
