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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 6534g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6534.b3 | 6534g1 | \([1, -1, 0, 159, 501]\) | \(9261/8\) | \(-382657176\) | \([]\) | \(2700\) | \(0.33444\) | \(\Gamma_0(N)\)-optimal |
| 6534.b2 | 6534g2 | \([1, -1, 0, -1656, -33984]\) | \(-1167051/512\) | \(-220410533376\) | \([]\) | \(8100\) | \(0.88374\) | |
| 6534.b1 | 6534g3 | \([1, -1, 0, -3471, 80603]\) | \(-132651/2\) | \(-69739270326\) | \([]\) | \(8100\) | \(0.88374\) |
Rank
sage: E.rank()
The elliptic curves in class 6534g have rank \(0\).
Complex multiplication
The elliptic curves in class 6534g do not have complex multiplication.Modular form 6534.2.a.g
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.
\(\left(\begin{array}{rrr} 1 & 3 & 3 \\ 3 & 1 & 9 \\ 3 & 9 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
