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SageMath
E = EllipticCurve("ce1")
E.isogeny_class()
Elliptic curves in class 195195ce
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
195195.cd2 | 195195ce1 | \([0, 1, 1, -1510916, 836633165]\) | \(-79028701534867456/16987307596875\) | \(-81994489194364621875\) | \([]\) | \(11520000\) | \(2.5422\) | \(\Gamma_0(N)\)-optimal |
195195.cd1 | 195195ce2 | \([0, 1, 1, -4527566, -70104469795]\) | \(-2126464142970105856/438611057788643355\) | \(-2117091801233743843704195\) | \([]\) | \(57600000\) | \(3.3470\) |
Rank
sage: E.rank()
The elliptic curves in class 195195ce have rank \(0\).
Complex multiplication
The elliptic curves in class 195195ce do not have complex multiplication.Modular form 195195.2.a.ce
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.