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SageMath
E = EllipticCurve("hh1")
E.isogeny_class()
Elliptic curves in class 302016hh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 302016.hh4 | 302016hh1 | \([0, 1, 0, -11172, -68598]\) | \(1360251712/771147\) | \(87432572829888\) | \([2]\) | \(983040\) | \(1.3651\) | \(\Gamma_0(N)\)-optimal |
| 302016.hh2 | 302016hh2 | \([0, 1, 0, -113417, 14593335]\) | \(22235451328/123201\) | \(893985123373056\) | \([2, 2]\) | \(1966080\) | \(1.7117\) | |
| 302016.hh1 | 302016hh3 | \([0, 1, 0, -1812257, 938422527]\) | \(11339065490696/351\) | \(20375729307648\) | \([2]\) | \(3932160\) | \(2.0582\) | |
| 302016.hh3 | 302016hh4 | \([0, 1, 0, -50497, 30763775]\) | \(-245314376/6908733\) | \(-401055479962435584\) | \([2]\) | \(3932160\) | \(2.0582\) |
Rank
sage: E.rank()
The elliptic curves in class 302016hh have rank \(0\).
Complex multiplication
The elliptic curves in class 302016hh do not have complex multiplication.Modular form 302016.2.a.hh
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
