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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 317898o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 317898.o3 | 317898o1 | \([1, -1, 0, 8673, 189133]\) | \(4492125/3584\) | \(-57559863126528\) | \([]\) | \(898128\) | \(1.3282\) | \(\Gamma_0(N)\)-optimal |
| 317898.o2 | 317898o2 | \([1, -1, 0, -92247, -13784923]\) | \(-7414875/2744\) | \(-32126497980354792\) | \([]\) | \(2694384\) | \(1.8775\) | |
| 317898.o1 | 317898o3 | \([1, -1, 0, -8039697, -8772192721]\) | \(-545407363875/14\) | \(-1475196335832618\) | \([]\) | \(8083152\) | \(2.4268\) |
Rank
sage: E.rank()
The elliptic curves in class 317898o have rank \(0\).
Complex multiplication
The elliptic curves in class 317898o do not have complex multiplication.Modular form 317898.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
