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SageMath
E = EllipticCurve("co1")
E.isogeny_class()
Elliptic curves in class 9450.co
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9450.co1 | 9450cb2 | \([1, -1, 1, -1212815, 501036247]\) | \(44548516344270315/1322306994176\) | \(5856067927432396800\) | \([]\) | \(233280\) | \(2.3781\) | |
9450.co2 | 9450cb1 | \([1, -1, 1, -1204040, 508822507]\) | \(392296847395243635/10976\) | \(5401015200\) | \([]\) | \(77760\) | \(1.8288\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9450.co have rank \(0\).
Complex multiplication
The elliptic curves in class 9450.co do not have complex multiplication.Modular form 9450.2.a.co
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.