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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 99846o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 99846.j2 | 99846o1 | \([1, -1, 1, -5894, -174933]\) | \(-132651/2\) | \(-341353604646\) | \([]\) | \(154224\) | \(1.0161\) | \(\Gamma_0(N)\)-optimal |
| 99846.j3 | 99846o2 | \([1, -1, 1, 21841, -877553]\) | \(9261/8\) | \(-995387111147736\) | \([]\) | \(462672\) | \(1.5654\) | |
| 99846.j1 | 99846o3 | \([1, -1, 1, -227774, 55535437]\) | \(-1167051/512\) | \(-573342976021095936\) | \([]\) | \(1388016\) | \(2.1147\) |
Rank
sage: E.rank()
The elliptic curves in class 99846o have rank \(1\).
Complex multiplication
The elliptic curves in class 99846o do not have complex multiplication.Modular form 99846.2.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.
