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SageMath
E = EllipticCurve("hh1")
E.isogeny_class()
Elliptic curves in class 254016hh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 254016.hh2 | 254016hh1 | \([0, 0, 0, 13524, -60368]\) | \(109503/64\) | \(-159879637499904\) | \([]\) | \(663552\) | \(1.4149\) | \(\Gamma_0(N)\)-optimal |
| 254016.hh1 | 254016hh2 | \([0, 0, 0, -174636, 30672432]\) | \(-35937/4\) | \(-65560643852304384\) | \([]\) | \(1990656\) | \(1.9642\) |
Rank
sage: E.rank()
The elliptic curves in class 254016hh have rank \(0\).
Complex multiplication
The elliptic curves in class 254016hh do not have complex multiplication.Modular form 254016.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
