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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 363090j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 363090.j4 | 363090j1 | \([1, 1, 0, 126542, -14298752]\) | \(1904733377263079/1858566937500\) | \(-218658541629937500\) | \([2]\) | \(4644864\) | \(2.0142\) | \(\Gamma_0(N)\)-optimal |
| 363090.j3 | 363090j2 | \([1, 1, 0, -669708, -131029002]\) | \(282353350636276921/100625101463250\) | \(11838442562049899250\) | \([2]\) | \(9289728\) | \(2.3608\) | |
| 363090.j2 | 363090j3 | \([1, 1, 0, -1288333, 786700573]\) | \(-2010112629576334921/1112397986481600\) | \(-130872510711573758400\) | \([2]\) | \(13934592\) | \(2.5635\) | |
| 363090.j1 | 363090j4 | \([1, 1, 0, -22818933, 41940289413]\) | \(11169185436600174776521/1823266881825480\) | \(214505525379885896520\) | \([2]\) | \(27869184\) | \(2.9101\) |
Rank
sage: E.rank()
The elliptic curves in class 363090j have rank \(0\).
Complex multiplication
The elliptic curves in class 363090j do not have complex multiplication.Modular form 363090.2.a.j
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
