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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 162.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
162.d1 | 162d2 | \([1, -1, 1, -56, -161]\) | \(-35937/4\) | \(-2125764\) | \([]\) | \(36\) | \(-0.048500\) | |
162.d2 | 162d1 | \([1, -1, 1, 4, -1]\) | \(109503/64\) | \(-5184\) | \([3]\) | \(12\) | \(-0.59781\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 162.d have rank \(0\).
Complex multiplication
The elliptic curves in class 162.d do not have complex multiplication.Modular form 162.2.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 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.