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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 33327o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 33327.g2 | 33327o1 | \([1, -1, 1, 2520850, -6746521084]\) | \(1349232625/15752961\) | \(-20684272483052101776447\) | \([2]\) | \(1554432\) | \(2.9629\) | \(\Gamma_0(N)\)-optimal |
| 33327.g1 | 33327o2 | \([1, -1, 1, -41827865, -97058244310]\) | \(6163717745375/466948881\) | \(613122694219853041546287\) | \([2]\) | \(3108864\) | \(3.3095\) |
Rank
sage: E.rank()
The elliptic curves in class 33327o have rank \(0\).
Complex multiplication
The elliptic curves in class 33327o do not have complex multiplication.Modular form 33327.2.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.
