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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 221067m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 221067.d2 | 221067m1 | \([1, -1, 1, -2448821, 5496029740]\) | \(-46574399618739/347190316781\) | \(-12106399678279866570303\) | \([2]\) | \(12856320\) | \(2.9204\) | \(\Gamma_0(N)\)-optimal |
| 221067.d1 | 221067m2 | \([1, -1, 1, -64080776, 196998840316]\) | \(834563889111074499/2244268390133\) | \(78256819971791059046679\) | \([2]\) | \(25712640\) | \(3.2669\) |
Rank
sage: E.rank()
The elliptic curves in class 221067m have rank \(1\).
Complex multiplication
The elliptic curves in class 221067m do not have complex multiplication.Modular form 221067.2.a.m
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.
