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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 9450.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9450.g1 | 9450e2 | \([1, -1, 0, -220767, -39869299]\) | \(268691220631875/7529536\) | \(33345867844800\) | \([]\) | \(46656\) | \(1.6971\) | |
9450.g2 | 9450e1 | \([1, -1, 0, -4767, 38861]\) | \(24348886875/12845056\) | \(6320730931200\) | \([]\) | \(15552\) | \(1.1478\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9450.g have rank \(1\).
Complex multiplication
The elliptic curves in class 9450.g do not have complex multiplication.Modular form 9450.2.a.g
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.