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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 236992.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
236992.f1 | 236992f2 | \([0, 1, 0, -85345, 9452799]\) | \(3543122/49\) | \(950764642107392\) | \([2]\) | \(1441792\) | \(1.6797\) | |
236992.f2 | 236992f1 | \([0, 1, 0, -705, 396319]\) | \(-4/7\) | \(-67911760150528\) | \([2]\) | \(720896\) | \(1.3331\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 236992.f have rank \(2\).
Complex multiplication
The elliptic curves in class 236992.f do not have complex multiplication.Modular form 236992.2.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.