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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 67600bo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
67600.ch2 | 67600bo1 | \([0, 1, 0, -128158, -17364437]\) | \(1141504/25\) | \(5098317006250000\) | \([]\) | \(359424\) | \(1.8021\) | \(\Gamma_0(N)\)-optimal |
67600.ch1 | 67600bo2 | \([0, 1, 0, -1226658, 515408063]\) | \(1000939264/15625\) | \(3186448128906250000\) | \([]\) | \(1078272\) | \(2.3514\) |
Rank
sage: E.rank()
The elliptic curves in class 67600bo have rank \(0\).
Complex multiplication
The elliptic curves in class 67600bo do not have complex multiplication.Modular form 67600.2.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.