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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 287490m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 287490.m6 | 287490m1 | \([1, 1, 0, 13662, -854412]\) | \(109902239/188160\) | \(-482767081117440\) | \([2]\) | \(1658880\) | \(1.5025\) | \(\Gamma_0(N)\)-optimal |
| 287490.m5 | 287490m2 | \([1, 1, 0, -95858, -8936988]\) | \(37966934881/8643600\) | \(22177112788832400\) | \([2, 2]\) | \(3317760\) | \(1.8491\) | |
| 287490.m4 | 287490m3 | \([1, 1, 0, -506558, 130947432]\) | \(5602762882081/345888060\) | \(887454130099776540\) | \([2]\) | \(6635520\) | \(2.1956\) | |
| 287490.m2 | 287490m4 | \([1, 1, 0, -1437478, -663915872]\) | \(128031684631201/9922500\) | \(25458420293302500\) | \([2, 2]\) | \(6635520\) | \(2.1956\) | |
| 287490.m3 | 287490m5 | \([1, 1, 0, -1341648, -756123498]\) | \(-104094944089921/35880468750\) | \(-92059466239174218750\) | \([2]\) | \(13271040\) | \(2.5422\) | |
| 287490.m1 | 287490m6 | \([1, 1, 0, -22999228, -42463524422]\) | \(524388516989299201/3150\) | \(8082038188350\) | \([2]\) | \(13271040\) | \(2.5422\) |
Rank
sage: E.rank()
The elliptic curves in class 287490m have rank \(0\).
Complex multiplication
The elliptic curves in class 287490m do not have complex multiplication.Modular form 287490.2.a.m
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 Cremona numbering.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
