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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 169050.bh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
169050.bh1 | 169050ir1 | \([1, 1, 0, -137550375, -620984596875]\) | \(156567200830221067489/16905000000\) | \(31075880390625000000\) | \([2]\) | \(20127744\) | \(3.1671\) | \(\Gamma_0(N)\)-optimal |
169050.bh2 | 169050ir2 | \([1, 1, 0, -137207375, -624235207875]\) | \(-155398856216042825569/1627294921875000\) | \(-2991400316619873046875000\) | \([2]\) | \(40255488\) | \(3.5137\) |
Rank
sage: E.rank()
The elliptic curves in class 169050.bh have rank \(0\).
Complex multiplication
The elliptic curves in class 169050.bh do not have complex multiplication.Modular form 169050.2.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.