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SageMath
E = EllipticCurve("ih1")
E.isogeny_class()
Elliptic curves in class 202800ih
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 202800.je2 | 202800ih1 | \([0, 1, 0, -1408, -13202812]\) | \(-4/975\) | \(-75298220400000000\) | \([2]\) | \(1548288\) | \(1.9172\) | \(\Gamma_0(N)\)-optimal |
| 202800.je1 | 202800ih2 | \([0, 1, 0, -846408, -295432812]\) | \(434163602/7605\) | \(1174652238240000000\) | \([2]\) | \(3096576\) | \(2.2638\) |
Rank
sage: E.rank()
The elliptic curves in class 202800ih have rank \(0\).
Complex multiplication
The elliptic curves in class 202800ih do not have complex multiplication.Modular form 202800.2.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 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.
