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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 18810h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18810.g1 | 18810h1 | \([1, -1, 0, -218709, 34270965]\) | \(1587074323222816849/224665436160000\) | \(163781102960640000\) | \([2]\) | \(221184\) | \(2.0290\) | \(\Gamma_0(N)\)-optimal |
| 18810.g2 | 18810h2 | \([1, -1, 0, 357291, 183915765]\) | \(6919293138571999151/24068144896012800\) | \(-17545677629193331200\) | \([2]\) | \(442368\) | \(2.3756\) |
Rank
sage: E.rank()
The elliptic curves in class 18810h have rank \(0\).
Complex multiplication
The elliptic curves in class 18810h do not have complex multiplication.Modular form 18810.2.a.h
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.
