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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 15810u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15810.u1 | 15810u1 | \([1, 0, 0, -35358150, 80924422500]\) | \(-4888687926204690735691893601/169462737117000000000\) | \(-169462737117000000000\) | \([9]\) | \(1329696\) | \(2.9723\) | \(\Gamma_0(N)\)-optimal |
| 15810.u2 | 15810u2 | \([1, 0, 0, -8493150, 199943095500]\) | \(-67753244699395599279333601/17231081514402384417573000\) | \(-17231081514402384417573000\) | \([3]\) | \(3989088\) | \(3.5216\) | |
| 15810.u3 | 15810u3 | \([1, 0, 0, 76411200, -5387747131230]\) | \(49339503184159010517017932799/12568600467346487856214473570\) | \(-12568600467346487856214473570\) | \([]\) | \(11967264\) | \(4.0709\) |
Rank
sage: E.rank()
The elliptic curves in class 15810u have rank \(1\).
Complex multiplication
The elliptic curves in class 15810u do not have complex multiplication.Modular form 15810.2.a.u
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.
