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SageMath
E = EllipticCurve("da1")
E.isogeny_class()
Elliptic curves in class 179520.da
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
179520.da1 | 179520gz2 | \([0, -1, 0, -752959105, -7952276846975]\) | \(-180093466903641160790448289/4344384000\) | \(-1138854199296000\) | \([]\) | \(26127360\) | \(3.3365\) | |
179520.da2 | 179520gz1 | \([0, -1, 0, -9289345, -10921605503]\) | \(-338173143620095981729/979226371031040\) | \(-256698317807560949760\) | \([]\) | \(8709120\) | \(2.7872\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 179520.da have rank \(0\).
Complex multiplication
The elliptic curves in class 179520.da do not have complex multiplication.Modular form 179520.2.a.da
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.