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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 144026.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
144026.d1 | 144026k2 | \([1, 1, 0, -2169, 37985]\) | \(1129315234499353/205381076\) | \(205381076\) | \([2]\) | \(111616\) | \(0.59836\) | |
144026.d2 | 144026k1 | \([1, 1, 0, -149, 413]\) | \(369682454233/116373008\) | \(116373008\) | \([2]\) | \(55808\) | \(0.25178\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 144026.d have rank \(1\).
Complex multiplication
The elliptic curves in class 144026.d do not have complex multiplication.Modular form 144026.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.