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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 48510o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 48510.f2 | 48510o1 | \([1, -1, 0, -2655, -36275]\) | \(57954303169/17036800\) | \(608571532800\) | \([]\) | \(77760\) | \(0.96704\) | \(\Gamma_0(N)\)-optimal |
| 48510.f1 | 48510o2 | \([1, -1, 0, -196695, -33527579]\) | \(23560326604350529/1375000\) | \(49116375000\) | \([]\) | \(233280\) | \(1.5163\) |
Rank
sage: E.rank()
The elliptic curves in class 48510o have rank \(1\).
Complex multiplication
The elliptic curves in class 48510o do not have complex multiplication.Modular form 48510.2.a.o
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.
