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SageMath
E = EllipticCurve("dc1")
E.isogeny_class()
Elliptic curves in class 115920.dc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 115920.dc1 | 115920ej4 | \([0, 0, 0, -434110827, 9550427546]\) | \(3029968325354577848895529/1753440696000000000000\) | \(5235745863204864000000000000\) | \([2]\) | \(53084160\) | \(4.0082\) | |
| 115920.dc2 | 115920ej2 | \([0, 0, 0, -298633467, 1986339218474]\) | \(986396822567235411402169/6336721794060000\) | \(18921349889514455040000\) | \([2]\) | \(17694720\) | \(3.4589\) | |
| 115920.dc3 | 115920ej1 | \([0, 0, 0, -18305787, 32287092266]\) | \(-227196402372228188089/19338934824115200\) | \(-57745749961850801356800\) | \([2]\) | \(8847360\) | \(3.1124\) | \(\Gamma_0(N)\)-optimal |
| 115920.dc4 | 115920ej3 | \([0, 0, 0, 108527253, 1193801114]\) | \(47342661265381757089751/27397579603968000000\) | \(-81808734336174784512000000\) | \([2]\) | \(26542080\) | \(3.6617\) |
Rank
sage: E.rank()
The elliptic curves in class 115920.dc have rank \(1\).
Complex multiplication
The elliptic curves in class 115920.dc do not have complex multiplication.Modular form 115920.2.a.dc
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
