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SageMath
E = EllipticCurve("oc1")
E.isogeny_class()
Elliptic curves in class 369600.oc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 369600.oc1 | 369600oc4 | \([0, 1, 0, -8132033, -8928503937]\) | \(116158555210501448/4764375\) | \(2439360000000000\) | \([2]\) | \(9437184\) | \(2.4394\) | |
| 369600.oc2 | 369600oc3 | \([0, 1, 0, -824033, 53280063]\) | \(120861530858888/67523047515\) | \(34571800327680000000\) | \([2]\) | \(9437184\) | \(2.4394\) | |
| 369600.oc3 | 369600oc2 | \([0, 1, 0, -509033, -139184937]\) | \(227919983840704/1452753225\) | \(92976206400000000\) | \([2, 2]\) | \(4718592\) | \(2.0928\) | |
| 369600.oc4 | 369600oc1 | \([0, 1, 0, -12908, -4735062]\) | \(-237867017536/9530541405\) | \(-9530541405000000\) | \([2]\) | \(2359296\) | \(1.7462\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 369600.oc have rank \(0\).
Complex multiplication
The elliptic curves in class 369600.oc do not have complex multiplication.Modular form 369600.2.a.oc
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
