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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 221952o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 221952.l2 | 221952o1 | \([0, -1, 0, -963, 49815]\) | \(-8000/81\) | \(-1001033261568\) | \([2]\) | \(327680\) | \(0.98489\) | \(\Gamma_0(N)\)-optimal |
| 221952.l1 | 221952o2 | \([0, -1, 0, -26973, 1709253]\) | \(2744000/9\) | \(7118458748928\) | \([2]\) | \(655360\) | \(1.3315\) |
Rank
sage: E.rank()
The elliptic curves in class 221952o have rank \(0\).
Complex multiplication
The elliptic curves in class 221952o do not have complex multiplication.Modular form 221952.2.a.o
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.
