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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 26928bo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
26928.s2 | 26928bo1 | \([0, 0, 0, -59297331, -168931514126]\) | \(7722211175253055152433/340131399900069888\) | \(1015626917999210284449792\) | \([2]\) | \(3115008\) | \(3.3695\) | \(\Gamma_0(N)\)-optimal |
26928.s1 | 26928bo2 | \([0, 0, 0, -159567411, 553033115890]\) | \(150476552140919246594353/42832838728685592576\) | \(127898171118435520462454784\) | \([2]\) | \(6230016\) | \(3.7161\) |
Rank
sage: E.rank()
The elliptic curves in class 26928bo have rank \(0\).
Complex multiplication
The elliptic curves in class 26928bo do not have complex multiplication.Modular form 26928.2.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.