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SageMath
E = EllipticCurve("dh1")
E.isogeny_class()
Elliptic curves in class 142800.dh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
142800.dh1 | 142800ds2 | \([0, -1, 0, -207408, -26714688]\) | \(15417797707369/4080067320\) | \(261124308480000000\) | \([2]\) | \(1327104\) | \(2.0506\) | |
142800.dh2 | 142800ds1 | \([0, -1, 0, 32592, -2714688]\) | \(59822347031/83966400\) | \(-5373849600000000\) | \([2]\) | \(663552\) | \(1.7040\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 142800.dh have rank \(1\).
Complex multiplication
The elliptic curves in class 142800.dh do not have complex multiplication.Modular form 142800.2.a.dh
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.