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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 409101bh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
409101.bh2 | 409101bh1 | \([1, 1, 0, -58566, 9742671]\) | \(-36561310759/46662561\) | \(-28354291617108303\) | \([2]\) | \(2764800\) | \(1.8502\) | \(\Gamma_0(N)\)-optimal* |
409101.bh1 | 409101bh2 | \([1, 1, 0, -1130021, 461682390]\) | \(262623524091319/134454573\) | \(81700705884869379\) | \([2]\) | \(5529600\) | \(2.1967\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 409101bh have rank \(1\).
Complex multiplication
The elliptic curves in class 409101bh do not have complex multiplication.Modular form 409101.2.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 Cremona 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 Cremona labels.