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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 95550.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 95550.q1 | 95550br6 | \([1, 1, 0, -74927150, 249604583250]\) | \(25306558948218234961/4478906250\) | \(8233419396972656250\) | \([2]\) | \(9437184\) | \(3.0261\) | |
| 95550.q2 | 95550br4 | \([1, 1, 0, -4697900, 3872437500]\) | \(6237734630203441/82168222500\) | \(151047018889101562500\) | \([2, 2]\) | \(4718592\) | \(2.6795\) | |
| 95550.q3 | 95550br5 | \([1, 1, 0, -716650, 10230493750]\) | \(-22143063655441/24584858584650\) | \(-45193500431648247656250\) | \([2]\) | \(9437184\) | \(3.0261\) | |
| 95550.q4 | 95550br2 | \([1, 1, 0, -557400, -65178000]\) | \(10418796526321/5038160400\) | \(9261477076556250000\) | \([2, 2]\) | \(2359296\) | \(2.3330\) | |
| 95550.q5 | 95550br1 | \([1, 1, 0, -459400, -119960000]\) | \(5832972054001/4542720\) | \(8350726020000000\) | \([2]\) | \(1179648\) | \(1.9864\) | \(\Gamma_0(N)\)-optimal |
| 95550.q6 | 95550br3 | \([1, 1, 0, 2015100, -494785500]\) | \(492271755328079/342606902820\) | \(-629802492341721562500\) | \([2]\) | \(4718592\) | \(2.6795\) |
Rank
sage: E.rank()
The elliptic curves in class 95550.q have rank \(1\).
Complex multiplication
The elliptic curves in class 95550.q do not have complex multiplication.Modular form 95550.2.a.q
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
