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SageMath
E = EllipticCurve("db1")
E.isogeny_class()
Elliptic curves in class 333270.db
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 333270.db1 | 333270db4 | \([1, -1, 1, -14352789218, 1819214009057]\) | \(3029968325354577848895529/1753440696000000000000\) | \(189228098983790144376000000000000\) | \([2]\) | \(1167851520\) | \(4.8828\) | |
| 333270.db2 | 333270db2 | \([1, -1, 1, -9873569003, 377624175754331]\) | \(986396822567235411402169/6336721794060000\) | \(683847375970293977098860000\) | \([2]\) | \(389283840\) | \(4.3335\) | |
| 333270.db3 | 333270db1 | \([1, -1, 1, -605235083, 6138230240027]\) | \(-227196402372228188089/19338934824115200\) | \(-2087022322161694205130931200\) | \([2]\) | \(194641920\) | \(3.9870\) | \(\Gamma_0(N)\)-optimal |
| 333270.db4 | 333270db3 | \([1, -1, 1, 3588182302, 226055738081]\) | \(47342661265381757089751/27397579603968000000\) | \(-2956696463725698018705408000000\) | \([2]\) | \(583925760\) | \(4.5363\) |
Rank
sage: E.rank()
The elliptic curves in class 333270.db have rank \(0\).
Complex multiplication
The elliptic curves in class 333270.db do not have complex multiplication.Modular form 333270.2.a.db
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.
