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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 107184.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 107184.p1 | 107184bw4 | \([0, -1, 0, -138264, -19742160]\) | \(71366476613135257/1143673377\) | \(4684486152192\) | \([2]\) | \(458752\) | \(1.5643\) | |
| 107184.p2 | 107184bw3 | \([0, -1, 0, -34424, 2163504]\) | \(1101438820807417/148956693039\) | \(610126614687744\) | \([2]\) | \(458752\) | \(1.5643\) | |
| 107184.p3 | 107184bw2 | \([0, -1, 0, -8904, -286416]\) | \(19061979249097/2198953449\) | \(9006913327104\) | \([2, 2]\) | \(229376\) | \(1.2177\) | |
| 107184.p4 | 107184bw1 | \([0, -1, 0, 776, -23120]\) | \(12600539783/62414583\) | \(-255650131968\) | \([2]\) | \(114688\) | \(0.87117\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 107184.p have rank \(2\).
Complex multiplication
The elliptic curves in class 107184.p do not have complex multiplication.Modular form 107184.2.a.p
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.
