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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 33810.v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 33810.v1 | 33810t4 | \([1, 1, 0, -147718267, -1957264931]\) | \(3029968325354577848895529/1753440696000000000000\) | \(206290544443704000000000000\) | \([2]\) | \(13271040\) | \(3.7387\) | |
| 33810.v2 | 33810t2 | \([1, 1, 0, -101618332, -394321479824]\) | \(986396822567235411402169/6336721794060000\) | \(745508982349364940000\) | \([2]\) | \(4423680\) | \(3.1894\) | |
| 33810.v3 | 33810t1 | \([1, 1, 0, -6229052, -6411433776]\) | \(-227196402372228188089/19338934824115200\) | \(-2275206343122329164800\) | \([2]\) | \(2211840\) | \(2.8429\) | \(\Gamma_0(N)\)-optimal |
| 33810.v4 | 33810t3 | \([1, 1, 0, 36929413, -221576739]\) | \(47342661265381757089751/27397579603968000000\) | \(-3223297842827231232000000\) | \([2]\) | \(6635520\) | \(3.3922\) |
Rank
sage: E.rank()
The elliptic curves in class 33810.v have rank \(0\).
Complex multiplication
The elliptic curves in class 33810.v do not have complex multiplication.Modular form 33810.2.a.v
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.
