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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 133952.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
133952.o1 | 133952bt2 | \([0, 1, 0, -6273, -132641]\) | \(104154702625/32188247\) | \(8437955821568\) | \([2]\) | \(245760\) | \(1.1849\) | |
133952.o2 | 133952bt1 | \([0, 1, 0, 1087, -13409]\) | \(541343375/625807\) | \(-164051550208\) | \([2]\) | \(122880\) | \(0.83830\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 133952.o have rank \(1\).
Complex multiplication
The elliptic curves in class 133952.o do not have complex multiplication.Modular form 133952.2.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 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.