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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 443646.bh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
443646.bh1 | 443646bh2 | \([1, -1, 1, -14195, 151435]\) | \(3687953625/2024072\) | \(173596804064712\) | \([2]\) | \(1548288\) | \(1.4230\) | \(\Gamma_0(N)\)-optimal* |
443646.bh2 | 443646bh1 | \([1, -1, 1, 3445, 17371]\) | \(52734375/32192\) | \(-2760982967232\) | \([2]\) | \(774144\) | \(1.0764\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 443646.bh have rank \(1\).
Complex multiplication
The elliptic curves in class 443646.bh do not have complex multiplication.Modular form 443646.2.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.