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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 244398.bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 244398.bq1 | 244398bq5 | \([1, 0, 0, -36435982737, 2676968999845767]\) | \(36136672427711016379227705697/1011258101510224722\) | \(149702492065518359311047858\) | \([2]\) | \(432537600\) | \(4.5333\) | |
| 244398.bq2 | 244398bq4 | \([1, 0, 0, -2607506607, -51149035842723]\) | \(13244420128496241770842177/29965867631164664892\) | \(4436023854435785272674308988\) | \([2]\) | \(216268800\) | \(4.1868\) | |
| 244398.bq3 | 244398bq3 | \([1, 0, 0, -2280140247, 41715959540805]\) | \(8856076866003496152467137/46664863048067576004\) | \(6908074486383933345827207556\) | \([2, 2]\) | \(216268800\) | \(4.1868\) | |
| 244398.bq4 | 244398bq6 | \([1, 0, 0, -1046041437, 86696146147923]\) | \(-855073332201294509246497/21439133060285771735058\) | \(-3173761121968694812850383496562\) | \([2]\) | \(432537600\) | \(4.5333\) | |
| 244398.bq5 | 244398bq2 | \([1, 0, 0, -222531267, -162556029135]\) | \(8232463578739844255617/4687062591766850064\) | \(693853477570849729953946896\) | \([2, 2]\) | \(108134400\) | \(3.8402\) | |
| 244398.bq6 | 244398bq1 | \([1, 0, 0, 55130253, -20226733983]\) | \(125177609053596564863/73635189229502208\) | \(-10900650699272584388742912\) | \([4]\) | \(54067200\) | \(3.4936\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 244398.bq have rank \(1\).
Complex multiplication
The elliptic curves in class 244398.bq do not have complex multiplication.Modular form 244398.2.a.bq
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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 4 & 8 \\ 8 & 1 & 4 & 8 & 2 & 4 \\ 2 & 4 & 1 & 2 & 2 & 4 \\ 4 & 8 & 2 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
