Show commands:
SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 100016i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
100016.n2 | 100016i1 | \([0, -1, 0, -1072, 9360]\) | \(133172077252/42875609\) | \(43904623616\) | \([2]\) | \(72192\) | \(0.74562\) | \(\Gamma_0(N)\)-optimal |
100016.n1 | 100016i2 | \([0, -1, 0, -15512, 748688]\) | \(201569651552306/39075001\) | \(80025602048\) | \([2]\) | \(144384\) | \(1.0922\) |
Rank
sage: E.rank()
The elliptic curves in class 100016i have rank \(1\).
Complex multiplication
The elliptic curves in class 100016i do not have complex multiplication.Modular form 100016.2.a.i
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.