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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 13923.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
13923.f1 | 13923a1 | \([1, -1, 0, -46809, 3909224]\) | \(420100556152674123/62939003491\) | \(1699353094257\) | \([2]\) | \(46080\) | \(1.3600\) | \(\Gamma_0(N)\)-optimal |
13923.f2 | 13923a2 | \([1, -1, 0, -42474, 4659179]\) | \(-313859434290315003/164114213839849\) | \(-4431083773675923\) | \([2]\) | \(92160\) | \(1.7066\) |
Rank
sage: E.rank()
The elliptic curves in class 13923.f have rank \(1\).
Complex multiplication
The elliptic curves in class 13923.f do not have complex multiplication.Modular form 13923.2.a.f
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.