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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 209484o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 209484.v2 | 209484o1 | \([0, 0, 0, -182505, -16510619]\) | \(736000/297\) | \(271285541698322448\) | \([]\) | \(1907712\) | \(2.0431\) | \(\Gamma_0(N)\)-optimal |
| 209484.v1 | 209484o2 | \([0, 0, 0, -6752685, 6753402853]\) | \(37280608000/3993\) | \(3647283393944112912\) | \([3]\) | \(5723136\) | \(2.5924\) |
Rank
sage: E.rank()
The elliptic curves in class 209484o have rank \(1\).
Complex multiplication
The elliptic curves in class 209484o do not have complex multiplication.Modular form 209484.2.a.o
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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
