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SageMath
E = EllipticCurve("hx1")
E.isogeny_class()
Elliptic curves in class 177600hx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 177600.l1 | 177600hx1 | \([0, -1, 0, -768133, -258854363]\) | \(3132662187311104/151723125\) | \(2427570000000000\) | \([2]\) | \(2064384\) | \(2.0248\) | \(\Gamma_0(N)\)-optimal |
| 177600.l2 | 177600hx2 | \([0, -1, 0, -727633, -287406863]\) | \(-166426126492624/43316015625\) | \(-11088900000000000000\) | \([2]\) | \(4128768\) | \(2.3714\) |
Rank
sage: E.rank()
The elliptic curves in class 177600hx have rank \(1\).
Complex multiplication
The elliptic curves in class 177600hx do not have complex multiplication.Modular form 177600.2.a.hx
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.
