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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 162624bx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 162624.c2 | 162624bx1 | \([0, -1, 0, -2625, 47841]\) | \(5735339/588\) | \(205161234432\) | \([2]\) | \(294912\) | \(0.90617\) | \(\Gamma_0(N)\)-optimal |
| 162624.c1 | 162624bx2 | \([0, -1, 0, -9665, -311199]\) | \(286191179/43218\) | \(15079350730752\) | \([2]\) | \(589824\) | \(1.2527\) |
Rank
sage: E.rank()
The elliptic curves in class 162624bx have rank \(1\).
Complex multiplication
The elliptic curves in class 162624bx do not have complex multiplication.Modular form 162624.2.a.bx
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.
