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SageMath
E = EllipticCurve("dk1")
E.isogeny_class()
Elliptic curves in class 101400.dk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
101400.dk1 | 101400dn1 | \([0, 1, 0, -1455783, 601225938]\) | \(621217777580032/74733890625\) | \(41047589425781250000\) | \([2]\) | \(2709504\) | \(2.4942\) | \(\Gamma_0(N)\)-optimal |
101400.dk2 | 101400dn2 | \([0, 1, 0, 2098092, 3081830688]\) | \(116227003261808/533935546875\) | \(-4692225585937500000000\) | \([2]\) | \(5419008\) | \(2.8407\) |
Rank
sage: E.rank()
The elliptic curves in class 101400.dk have rank \(0\).
Complex multiplication
The elliptic curves in class 101400.dk do not have complex multiplication.Modular form 101400.2.a.dk
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.