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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 24255bo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
24255.bx2 | 24255bo1 | \([0, 0, 1, -3942687, 3528777397]\) | \(-79028701534867456/16987307596875\) | \(-1456935478817800471875\) | \([]\) | \(2304000\) | \(2.7820\) | \(\Gamma_0(N)\)-optimal |
24255.bx1 | 24255bo2 | \([0, 0, 1, -11814537, -295504559933]\) | \(-2126464142970105856/438611057788643355\) | \(-37617969054238778410775955\) | \([]\) | \(11520000\) | \(3.5867\) |
Rank
sage: E.rank()
The elliptic curves in class 24255bo have rank \(0\).
Complex multiplication
The elliptic curves in class 24255bo do not have complex multiplication.Modular form 24255.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.