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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 236992.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 236992.q1 | 236992q6 | \([0, 1, 0, -92444513, -342144006113]\) | \(2251439055699625/25088\) | \(973582993517969408\) | \([2]\) | \(14598144\) | \(3.0206\) | |
| 236992.q2 | 236992q5 | \([0, 1, 0, -5773153, -5356435425]\) | \(-548347731625/1835008\) | \(-71210641811600048128\) | \([2]\) | \(7299072\) | \(2.6740\) | |
| 236992.q3 | 236992q4 | \([0, 1, 0, -1202593, -416472609]\) | \(4956477625/941192\) | \(36524574491197571072\) | \([2]\) | \(4866048\) | \(2.4713\) | |
| 236992.q4 | 236992q2 | \([0, 1, 0, -356193, 81650719]\) | \(128787625/98\) | \(3803058568429568\) | \([2]\) | \(1622016\) | \(1.9220\) | |
| 236992.q5 | 236992q1 | \([0, 1, 0, -17633, 1818271]\) | \(-15625/28\) | \(-1086588162408448\) | \([2]\) | \(811008\) | \(1.5754\) | \(\Gamma_0(N)\)-optimal |
| 236992.q6 | 236992q3 | \([0, 1, 0, 151647, -38097953]\) | \(9938375/21952\) | \(-851885119328223232\) | \([2]\) | \(2433024\) | \(2.1247\) |
Rank
sage: E.rank()
The elliptic curves in class 236992.q have rank \(0\).
Complex multiplication
The elliptic curves in class 236992.q do not have complex multiplication.Modular form 236992.2.a.q
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 18 & 6 \\ 2 & 1 & 6 & 18 & 9 & 3 \\ 3 & 6 & 1 & 3 & 6 & 2 \\ 9 & 18 & 3 & 1 & 2 & 6 \\ 18 & 9 & 6 & 2 & 1 & 3 \\ 6 & 3 & 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
