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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 39270.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
39270.j1 | 39270i2 | \([1, 1, 0, -414178793, -2525377035003]\) | \(7857552442072520325669578770969/1792478631174686569867737600\) | \(1792478631174686569867737600\) | \([2]\) | \(21288960\) | \(3.9420\) | |
39270.j2 | 39270i1 | \([1, 1, 0, 59106327, -244237413627]\) | \(22836293554064983709494580711/38990271813074615296327680\) | \(-38990271813074615296327680\) | \([2]\) | \(10644480\) | \(3.5954\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 39270.j have rank \(0\).
Complex multiplication
The elliptic curves in class 39270.j do not have complex multiplication.Modular form 39270.2.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 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.