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SageMath
E = EllipticCurve("ih1")
E.isogeny_class()
Elliptic curves in class 100800.ih
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
100800.ih1 | 100800og2 | \([0, 0, 0, -1233300, -527168000]\) | \(4446542056384/25725\) | \(1200225600000000\) | \([2]\) | \(1474560\) | \(2.0838\) | |
100800.ih2 | 100800og1 | \([0, 0, 0, -75675, -8552000]\) | \(-65743598656/5294205\) | \(-3859475445000000\) | \([2]\) | \(737280\) | \(1.7372\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 100800.ih have rank \(0\).
Complex multiplication
The elliptic curves in class 100800.ih do not have complex multiplication.Modular form 100800.2.a.ih
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 LMFDB 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 LMFDB labels.