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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 1290.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1290.n1 | 1290n3 | \([1, 0, 0, -34306, -1065280]\) | \(4465136636671380769/2096375976562500\) | \(2096375976562500\) | \([2]\) | \(8640\) | \(1.6342\) | |
| 1290.n2 | 1290n1 | \([1, 0, 0, -17566, 894596]\) | \(599437478278595809/33854760000\) | \(33854760000\) | \([6]\) | \(2880\) | \(1.0849\) | \(\Gamma_0(N)\)-optimal |
| 1290.n3 | 1290n2 | \([1, 0, 0, -16566, 1001196]\) | \(-502780379797811809/143268096832200\) | \(-143268096832200\) | \([6]\) | \(5760\) | \(1.4315\) | |
| 1290.n4 | 1290n4 | \([1, 0, 0, 121944, -8034030]\) | \(200541749524551119231/144008551960031250\) | \(-144008551960031250\) | \([2]\) | \(17280\) | \(1.9808\) |
Rank
sage: E.rank()
The elliptic curves in class 1290.n have rank \(0\).
Complex multiplication
The elliptic curves in class 1290.n do not have complex multiplication.Modular form 1290.2.a.n
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
