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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 54096.bi
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 54096.bi1 | 54096bw6 | \([0, -1, 0, -62041072, -188068013888]\) | \(54804145548726848737/637608031452\) | \(307257128109245841408\) | \([2]\) | \(4718592\) | \(3.0821\) | |
| 54096.bi2 | 54096bw4 | \([0, -1, 0, -13887792, 19924489152]\) | \(614716917569296417/19093020912\) | \(9200741651562037248\) | \([2]\) | \(2359296\) | \(2.7355\) | |
| 54096.bi3 | 54096bw3 | \([0, -1, 0, -3978032, -2777240640]\) | \(14447092394873377/1439452851984\) | \(693658372436236763136\) | \([2, 2]\) | \(2359296\) | \(2.7355\) | |
| 54096.bi4 | 54096bw2 | \([0, -1, 0, -904752, 283746240]\) | \(169967019783457/26337394944\) | \(12691735256132222976\) | \([2, 2]\) | \(1179648\) | \(2.3889\) | |
| 54096.bi5 | 54096bw1 | \([0, -1, 0, 98768, 24436672]\) | \(221115865823/664731648\) | \(-320327735933140992\) | \([2]\) | \(589824\) | \(2.0424\) | \(\Gamma_0(N)\)-optimal |
| 54096.bi6 | 54096bw5 | \([0, -1, 0, 4912528, -13438800192]\) | \(27207619911317663/177609314617308\) | \(-85588206614166195781632\) | \([4]\) | \(4718592\) | \(3.0821\) |
Rank
sage: E.rank()
The elliptic curves in class 54096.bi have rank \(0\).
Complex multiplication
The elliptic curves in class 54096.bi do not have complex multiplication.Modular form 54096.2.a.bi
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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
