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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 158.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
158.e1 | 158e2 | \([1, 1, 1, -9, 5]\) | \(81182737/12482\) | \(12482\) | \([2]\) | \(12\) | \(-0.49047\) | |
158.e2 | 158e1 | \([1, 1, 1, 1, 1]\) | \(103823/316\) | \(-316\) | \([2]\) | \(6\) | \(-0.83704\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 158.e have rank \(0\).
Complex multiplication
The elliptic curves in class 158.e do not have complex multiplication.Modular form 158.2.a.e
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.