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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 236691.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
236691.w1 | 236691w1 | \([1, -1, 0, -13527855, 19151906168]\) | \(420100556152674123/62939003491\) | \(41018252567991841233\) | \([2]\) | \(13271040\) | \(2.7766\) | \(\Gamma_0(N)\)-optimal |
236691.w2 | 236691w2 | \([1, -1, 0, -12275040, 22841446343]\) | \(-313859434290315003/164114213839849\) | \(-106955590331882975051187\) | \([2]\) | \(26542080\) | \(3.1232\) |
Rank
sage: E.rank()
The elliptic curves in class 236691.w have rank \(0\).
Complex multiplication
The elliptic curves in class 236691.w do not have complex multiplication.Modular form 236691.2.a.w
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.