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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 84966.y
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 84966.y1 | 84966s4 | \([1, 1, 0, -1867464, 883050498]\) | \(1246079601667529/137282971014\) | \(79350866513786560518\) | \([2]\) | \(3072000\) | \(2.5518\) | |
| 84966.y2 | 84966s2 | \([1, 1, 0, -426374, -107338188]\) | \(14830727012009/4704\) | \(2718956862048\) | \([2]\) | \(614400\) | \(1.7470\) | |
| 84966.y3 | 84966s1 | \([1, 1, 0, -26534, -1700460]\) | \(-3574558889/64512\) | \(-37288551250944\) | \([2]\) | \(307200\) | \(1.4005\) | \(\Gamma_0(N)\)-optimal |
| 84966.y4 | 84966s3 | \([1, 1, 0, 156726, 68921280]\) | \(736558976791/3969746172\) | \(-2294551146885242364\) | \([2]\) | \(1536000\) | \(2.2052\) |
Rank
sage: E.rank()
The elliptic curves in class 84966.y have rank \(0\).
Complex multiplication
The elliptic curves in class 84966.y do not have complex multiplication.Modular form 84966.2.a.y
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.
\(\left(\begin{array}{rrrr} 1 & 5 & 10 & 2 \\ 5 & 1 & 2 & 10 \\ 10 & 2 & 1 & 5 \\ 2 & 10 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
