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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 405042.bh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
405042.bh1 | 405042bh1 | \([1, 0, 1, -3257, 34460]\) | \(81182737/35904\) | \(1689135311424\) | \([2]\) | \(663552\) | \(1.0420\) | \(\Gamma_0(N)\)-optimal |
405042.bh2 | 405042bh2 | \([1, 0, 1, 11183, 259724]\) | \(3288008303/2517768\) | \(-118450613713608\) | \([2]\) | \(1327104\) | \(1.3886\) |
Rank
sage: E.rank()
The elliptic curves in class 405042.bh have rank \(2\).
Complex multiplication
The elliptic curves in class 405042.bh do not have complex multiplication.Modular form 405042.2.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.