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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 90650j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 90650.e3 | 90650j1 | \([1, 0, 1, -91901, 5855448]\) | \(46694890801/18944000\) | \(34824104000000000\) | \([2]\) | \(829440\) | \(1.8719\) | \(\Gamma_0(N)\)-optimal |
| 90650.e4 | 90650j2 | \([1, 0, 1, 300099, 42703448]\) | \(1625964918479/1369000000\) | \(-2516585640625000000\) | \([2]\) | \(1658880\) | \(2.2184\) | |
| 90650.e1 | 90650j3 | \([1, 0, 1, -6461901, 6321955448]\) | \(16232905099479601/4052240\) | \(7449093496250000\) | \([2]\) | \(2488320\) | \(2.4212\) | |
| 90650.e2 | 90650j4 | \([1, 0, 1, -6437401, 6372278448]\) | \(-16048965315233521/256572640900\) | \(-471648666081939062500\) | \([2]\) | \(4976640\) | \(2.7678\) |
Rank
sage: E.rank()
The elliptic curves in class 90650j have rank \(0\).
Complex multiplication
The elliptic curves in class 90650j do not have complex multiplication.Modular form 90650.2.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.
