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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 127050.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
127050.x1 | 127050bq2 | \([1, 1, 0, -9144940, 8731114000]\) | \(286960544769079/54235247808\) | \(15985484667460801416000\) | \([2]\) | \(14192640\) | \(2.9782\) | |
127050.x2 | 127050bq1 | \([1, 1, 0, -2756140, -1637908400]\) | \(7855676688439/619573248\) | \(182615163690871296000\) | \([2]\) | \(7096320\) | \(2.6316\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 127050.x have rank \(0\).
Complex multiplication
The elliptic curves in class 127050.x do not have complex multiplication.Modular form 127050.2.a.x
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.