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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 141570.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
141570.d1 | 141570do2 | \([1, -1, 0, -2414880, 1445015776]\) | \(1205943158724121/1258400\) | \(1625183292189600\) | \([2]\) | \(2764800\) | \(2.2086\) | |
141570.d2 | 141570do1 | \([1, -1, 0, -149760, 22973440]\) | \(-287626699801/9518080\) | \(-12292295446379520\) | \([2]\) | \(1382400\) | \(1.8620\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 141570.d have rank \(0\).
Complex multiplication
The elliptic curves in class 141570.d do not have complex multiplication.Modular form 141570.2.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.