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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 43890i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
43890.j2 | 43890i1 | \([1, 1, 0, 173, -359]\) | \(567457901639/408615900\) | \(-408615900\) | \([2]\) | \(21504\) | \(0.34074\) | \(\Gamma_0(N)\)-optimal |
43890.j1 | 43890i2 | \([1, 1, 0, -777, -3969]\) | \(51982817627161/24342754590\) | \(24342754590\) | \([2]\) | \(43008\) | \(0.68731\) |
Rank
sage: E.rank()
The elliptic curves in class 43890i have rank \(0\).
Complex multiplication
The elliptic curves in class 43890i do not have complex multiplication.Modular form 43890.2.a.i
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.