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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 11088.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11088.k1 | 11088br3 | \([0, 0, 0, -743571, -246792366]\) | \(15226621995131793/2324168\) | \(6939928461312\) | \([2]\) | \(73728\) | \(1.8696\) | |
11088.k2 | 11088br4 | \([0, 0, 0, -86931, 3788370]\) | \(24331017010833/12004097336\) | \(35844042579738624\) | \([2]\) | \(73728\) | \(1.8696\) | |
11088.k3 | 11088br2 | \([0, 0, 0, -46611, -3832110]\) | \(3750606459153/45914176\) | \(137098994909184\) | \([2, 2]\) | \(36864\) | \(1.5231\) | |
11088.k4 | 11088br1 | \([0, 0, 0, -531, -154926]\) | \(-5545233/3469312\) | \(-10359310123008\) | \([2]\) | \(18432\) | \(1.1765\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 11088.k have rank \(0\).
Complex multiplication
The elliptic curves in class 11088.k do not have complex multiplication.Modular form 11088.2.a.k
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.