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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 133952.bh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
133952.bh1 | 133952cg2 | \([0, 0, 0, -1340, 1584]\) | \(16241202000/9332687\) | \(152906743808\) | \([2]\) | \(92160\) | \(0.83572\) | |
133952.bh2 | 133952cg1 | \([0, 0, 0, -880, -10008]\) | \(73598976000/336973\) | \(345060352\) | \([2]\) | \(46080\) | \(0.48914\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 133952.bh have rank \(0\).
Complex multiplication
The elliptic curves in class 133952.bh do not have complex multiplication.Modular form 133952.2.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.