Show commands:
SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 9450.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9450.n1 | 9450ba2 | \([1, -1, 0, -29337, -1926739]\) | \(5674764464955/43904\) | \(21604060800\) | \([]\) | \(18144\) | \(1.1569\) | |
9450.n2 | 9450ba1 | \([1, -1, 0, -537, 301]\) | \(25397889795/14680064\) | \(9909043200\) | \([]\) | \(6048\) | \(0.60755\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9450.n have rank \(0\).
Complex multiplication
The elliptic curves in class 9450.n do not have complex multiplication.Modular form 9450.2.a.n
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.