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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 11550.bh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11550.bh1 | 11550bh2 | \([1, 0, 1, -8201, -285952]\) | \(31226116949/71148\) | \(138960937500\) | \([2]\) | \(25600\) | \(1.0196\) | |
11550.bh2 | 11550bh1 | \([1, 0, 1, -701, -952]\) | \(19465109/11088\) | \(21656250000\) | \([2]\) | \(12800\) | \(0.67304\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 11550.bh have rank \(0\).
Complex multiplication
The elliptic curves in class 11550.bh do not have complex multiplication.Modular form 11550.2.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.