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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 18240bx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18240.f2 | 18240bx1 | \([0, -1, 0, 55839, -4176639]\) | \(293798043977756/283988784375\) | \(-18611488972800000\) | \([2]\) | \(107520\) | \(1.8089\) | \(\Gamma_0(N)\)-optimal |
| 18240.f1 | 18240bx2 | \([0, -1, 0, -294081, -37698975]\) | \(21459330184836962/7710029296875\) | \(1010568960000000000\) | \([2]\) | \(215040\) | \(2.1555\) |
Rank
sage: E.rank()
The elliptic curves in class 18240bx have rank \(1\).
Complex multiplication
The elliptic curves in class 18240bx do not have complex multiplication.Modular form 18240.2.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.
