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SageMath
E = EllipticCurve("ku1")
E.isogeny_class()
Elliptic curves in class 277200.ku
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 277200.ku1 | 277200ku4 | \([0, 0, 0, -75273075, -251366604750]\) | \(1010962818911303721/57392720\) | \(2677714744320000000\) | \([2]\) | \(18874368\) | \(3.0026\) | |
| 277200.ku2 | 277200ku3 | \([0, 0, 0, -7881075, 2008307250]\) | \(1160306142246441/634128110000\) | \(29585881100160000000000\) | \([2]\) | \(18874368\) | \(3.0026\) | |
| 277200.ku3 | 277200ku2 | \([0, 0, 0, -4713075, -3912684750]\) | \(248158561089321/1859334400\) | \(86749105766400000000\) | \([2, 2]\) | \(9437184\) | \(2.6560\) | |
| 277200.ku4 | 277200ku1 | \([0, 0, 0, -105075, -138732750]\) | \(-2749884201/176619520\) | \(-8240360325120000000\) | \([2]\) | \(4718592\) | \(2.3094\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 277200.ku have rank \(0\).
Complex multiplication
The elliptic curves in class 277200.ku do not have complex multiplication.Modular form 277200.2.a.ku
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.
