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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 455175.bh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
455175.bh1 | 455175bh2 | \([1, -1, 1, -6937355, 6972648022]\) | \(4973940243/50575\) | \(375440170304070703125\) | \([2]\) | \(15925248\) | \(2.7657\) | \(\Gamma_0(N)\)-optimal* |
455175.bh2 | 455175bh1 | \([1, -1, 1, -109730, 267920272]\) | \(-19683/4165\) | \(-30918602260335234375\) | \([2]\) | \(7962624\) | \(2.4191\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 455175.bh have rank \(1\).
Complex multiplication
The elliptic curves in class 455175.bh do not have complex multiplication.Modular form 455175.2.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.