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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 202800.bh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
202800.bh1 | 202800ji1 | \([0, -1, 0, -1455783, -601225938]\) | \(621217777580032/74733890625\) | \(41047589425781250000\) | \([2]\) | \(5419008\) | \(2.4942\) | \(\Gamma_0(N)\)-optimal |
202800.bh2 | 202800ji2 | \([0, -1, 0, 2098092, -3081830688]\) | \(116227003261808/533935546875\) | \(-4692225585937500000000\) | \([2]\) | \(10838016\) | \(2.8407\) |
Rank
sage: E.rank()
The elliptic curves in class 202800.bh have rank \(0\).
Complex multiplication
The elliptic curves in class 202800.bh do not have complex multiplication.Modular form 202800.2.a.bh
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.