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SageMath
E = EllipticCurve("dc1")
E.isogeny_class()
Elliptic curves in class 108900.dc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 108900.dc1 | 108900bw4 | \([0, 0, 0, -6806150175, -216122709888250]\) | \(6749703004355978704/5671875\) | \(29300179546687500000000\) | \([2]\) | \(39813120\) | \(4.0465\) | |
| 108900.dc2 | 108900bw3 | \([0, 0, 0, -425290800, -3378477466375]\) | \(-26348629355659264/24169921875\) | \(-7803669978698730468750000\) | \([2]\) | \(19906560\) | \(3.7000\) | |
| 108900.dc3 | 108900bw2 | \([0, 0, 0, -85931175, -282320739250]\) | \(13584145739344/1195803675\) | \(6177368573899944300000000\) | \([2]\) | \(13271040\) | \(3.4972\) | |
| 108900.dc4 | 108900bw1 | \([0, 0, 0, 5953200, -20542154875]\) | \(72268906496/606436875\) | \(-195798449820739218750000\) | \([2]\) | \(6635520\) | \(3.1506\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 108900.dc have rank \(0\).
Complex multiplication
The elliptic curves in class 108900.dc do not have complex multiplication.Modular form 108900.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
