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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 29645o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 29645.g2 | 29645o1 | \([0, -1, 1, -7905, 302763]\) | \(-262144/35\) | \(-7294783303115\) | \([]\) | \(43200\) | \(1.2008\) | \(\Gamma_0(N)\)-optimal |
| 29645.g3 | 29645o2 | \([0, -1, 1, 51385, -782244]\) | \(71991296/42875\) | \(-8936109546315875\) | \([]\) | \(129600\) | \(1.7501\) | |
| 29645.g1 | 29645o3 | \([0, -1, 1, -778675, -276403667]\) | \(-250523582464/13671875\) | \(-2849524727779296875\) | \([]\) | \(388800\) | \(2.2994\) |
Rank
sage: E.rank()
The elliptic curves in class 29645o have rank \(0\).
Complex multiplication
The elliptic curves in class 29645o do not have complex multiplication.Modular form 29645.2.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.
