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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 182182.bh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
182182.bh1 | 182182e2 | \([1, 0, 0, -1942067, 1041541045]\) | \(1426487591593/2156\) | \(1224326107400396\) | \([2]\) | \(3317760\) | \(2.1631\) | |
182182.bh2 | 182182e1 | \([1, 0, 0, -120247, 16585113]\) | \(-338608873/13552\) | \(-7695764103659632\) | \([2]\) | \(1658880\) | \(1.8165\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 182182.bh have rank \(1\).
Complex multiplication
The elliptic curves in class 182182.bh do not have complex multiplication.Modular form 182182.2.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.