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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 200277r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 200277.r1 | 200277r1 | \([0, 0, 1, -232356, -43110347]\) | \(-78843215872/539\) | \(-9484399124739\) | \([]\) | \(921600\) | \(1.6709\) | \(\Gamma_0(N)\)-optimal |
| 200277.r2 | 200277r2 | \([0, 0, 1, -128316, -81800222]\) | \(-13278380032/156590819\) | \(-2755417118118299019\) | \([]\) | \(2764800\) | \(2.2202\) | |
| 200277.r3 | 200277r3 | \([0, 0, 1, 1146174, 2117332273]\) | \(9463555063808/115539436859\) | \(-2033065183336431457059\) | \([]\) | \(8294400\) | \(2.7695\) |
Rank
sage: E.rank()
The elliptic curves in class 200277r have rank \(0\).
Complex multiplication
The elliptic curves in class 200277r do not have complex multiplication.Modular form 200277.2.a.r
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
