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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 142912d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
142912.j2 | 142912d1 | \([0, 1, 0, 8799, -2009633]\) | \(287365339799/6841188508\) | \(-1793376520241152\) | \([2]\) | \(921600\) | \(1.6071\) | \(\Gamma_0(N)\)-optimal |
142912.j1 | 142912d2 | \([0, 1, 0, -195361, -31612833]\) | \(3145571940578761/180219208862\) | \(47243384287920128\) | \([2]\) | \(1843200\) | \(1.9537\) |
Rank
sage: E.rank()
The elliptic curves in class 142912d have rank \(1\).
Complex multiplication
The elliptic curves in class 142912d do not have complex multiplication.Modular form 142912.2.a.d
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.