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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 11088.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11088.u1 | 11088bf4 | \([0, 0, 0, -2035155, -1117413358]\) | \(312196988566716625/25367712678\) | \(75747584173105152\) | \([2]\) | \(110592\) | \(2.2840\) | |
| 11088.u2 | 11088bf3 | \([0, 0, 0, -118515, -19945294]\) | \(-61653281712625/21875235228\) | \(-65319102387044352\) | \([2]\) | \(55296\) | \(1.9374\) | |
| 11088.u3 | 11088bf2 | \([0, 0, 0, -52275, 2307314]\) | \(5290763640625/2291573592\) | \(6842602080534528\) | \([2]\) | \(36864\) | \(1.7347\) | |
| 11088.u4 | 11088bf1 | \([0, 0, 0, 11085, 267122]\) | \(50447927375/39517632\) | \(-117999016869888\) | \([2]\) | \(18432\) | \(1.3881\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 11088.u have rank \(1\).
Complex multiplication
The elliptic curves in class 11088.u do not have complex multiplication.Modular form 11088.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
