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SageMath
E = EllipticCurve("by1")
E.isogeny_class()
Elliptic curves in class 14490.by
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 14490.by1 | 14490ca4 | \([1, -1, 1, -27131927, -142442449]\) | \(3029968325354577848895529/1753440696000000000000\) | \(1278258267384000000000000\) | \([6]\) | \(2211840\) | \(3.3151\) | |
| 14490.by2 | 14490ca2 | \([1, -1, 1, -18664592, -31031884141]\) | \(986396822567235411402169/6336721794060000\) | \(4619470187869740000\) | \([2]\) | \(737280\) | \(2.7658\) | |
| 14490.by3 | 14490ca1 | \([1, -1, 1, -1144112, -504199789]\) | \(-227196402372228188089/19338934824115200\) | \(-14098083486779980800\) | \([2]\) | \(368640\) | \(2.4192\) | \(\Gamma_0(N)\)-optimal |
| 14490.by4 | 14490ca3 | \([1, -1, 1, 6782953, -20348881]\) | \(47342661265381757089751/27397579603968000000\) | \(-19972835531292672000000\) | \([6]\) | \(1105920\) | \(2.9685\) |
Rank
sage: E.rank()
The elliptic curves in class 14490.by have rank \(1\).
Complex multiplication
The elliptic curves in class 14490.by do not have complex multiplication.Modular form 14490.2.a.by
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.
