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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 16317g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16317.h3 | 16317g1 | \([0, 0, 1, -1470, 21523]\) | \(4096000/37\) | \(3173346477\) | \([]\) | \(7560\) | \(0.64573\) | \(\Gamma_0(N)\)-optimal |
| 16317.h2 | 16317g2 | \([0, 0, 1, -10290, -389048]\) | \(1404928000/50653\) | \(4344311327013\) | \([]\) | \(22680\) | \(1.1950\) | |
| 16317.h1 | 16317g3 | \([0, 0, 1, -826140, -289020461]\) | \(727057727488000/37\) | \(3173346477\) | \([]\) | \(68040\) | \(1.7443\) |
Rank
sage: E.rank()
The elliptic curves in class 16317g have rank \(0\).
Complex multiplication
The elliptic curves in class 16317g do not have complex multiplication.Modular form 16317.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
