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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 42350bo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
42350.f1 | 42350bo1 | \([1, 0, 1, -134676, -67505902]\) | \(-243979633825/1636214272\) | \(-1811658369949120000\) | \([]\) | \(622080\) | \(2.1868\) | \(\Gamma_0(N)\)-optimal |
42350.f2 | 42350bo2 | \([1, 0, 1, 1196324, 1693673298]\) | \(171015136702175/1218033273688\) | \(-1348637652729991855000\) | \([]\) | \(1866240\) | \(2.7361\) |
Rank
sage: E.rank()
The elliptic curves in class 42350bo have rank \(1\).
Complex multiplication
The elliptic curves in class 42350bo do not have complex multiplication.Modular form 42350.2.a.bo
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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.