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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 133200bo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
133200.h1 | 133200bo1 | \([0, 0, 0, -2100, 10375]\) | \(5619712/2997\) | \(546203250000\) | \([2]\) | \(196608\) | \(0.94352\) | \(\Gamma_0(N)\)-optimal |
133200.h2 | 133200bo2 | \([0, 0, 0, 8025, 81250]\) | \(19600688/12321\) | \(-35928036000000\) | \([2]\) | \(393216\) | \(1.2901\) |
Rank
sage: E.rank()
The elliptic curves in class 133200bo have rank \(0\).
Complex multiplication
The elliptic curves in class 133200bo do not have complex multiplication.Modular form 133200.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.