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SageMath
E = EllipticCurve("eu1")
E.isogeny_class()
Elliptic curves in class 162240.eu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
162240.eu1 | 162240fz2 | \([0, 1, 0, -497761, -121254145]\) | \(10779215329/1232010\) | \(1558885683977256960\) | \([2]\) | \(3096576\) | \(2.2232\) | |
162240.eu2 | 162240fz1 | \([0, 1, 0, 43039, -9524865]\) | \(6967871/35100\) | \(-44412697549209600\) | \([2]\) | \(1548288\) | \(1.8766\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 162240.eu have rank \(0\).
Complex multiplication
The elliptic curves in class 162240.eu do not have complex multiplication.Modular form 162240.2.a.eu
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.