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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 11088.bm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11088.bm1 | 11088bm3 | \([0, 0, 0, -32619, -2266598]\) | \(1285429208617/614922\) | \(1836147253248\) | \([2]\) | \(24576\) | \(1.3081\) | |
| 11088.bm2 | 11088bm4 | \([0, 0, 0, -18219, 930778]\) | \(223980311017/4278582\) | \(12775777394688\) | \([2]\) | \(24576\) | \(1.3081\) | |
| 11088.bm3 | 11088bm2 | \([0, 0, 0, -2379, -22790]\) | \(498677257/213444\) | \(637340368896\) | \([2, 2]\) | \(12288\) | \(0.96154\) | |
| 11088.bm4 | 11088bm1 | \([0, 0, 0, 501, -2630]\) | \(4657463/3696\) | \(-11036196864\) | \([2]\) | \(6144\) | \(0.61497\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 11088.bm have rank \(0\).
Complex multiplication
The elliptic curves in class 11088.bm do not have complex multiplication.Modular form 11088.2.a.bm
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.
