Show commands:
SageMath
E = EllipticCurve("kg1")
E.isogeny_class()
Elliptic curves in class 202800kg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
202800.ep1 | 202800kg1 | \([0, -1, 0, -246027383, -1321877495238]\) | \(621217777580032/74733890625\) | \(198128874068665769531250000\) | \([2]\) | \(70447104\) | \(3.7766\) | \(\Gamma_0(N)\)-optimal |
202800.ep2 | 202800kg2 | \([0, -1, 0, 354577492, -6769363711488]\) | \(116227003261808/533935546875\) | \(-22648476688233398437500000000\) | \([2]\) | \(140894208\) | \(4.1232\) |
Rank
sage: E.rank()
The elliptic curves in class 202800kg have rank \(0\).
Complex multiplication
The elliptic curves in class 202800kg do not have complex multiplication.Modular form 202800.2.a.kg
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 Cremona 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 Cremona labels.