Show commands:
SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 273273.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
273273.f1 | 273273f2 | \([1, 1, 1, -601728, 110725194]\) | \(14553591673375/5208653241\) | \(8623422799147523367\) | \([2]\) | \(5529600\) | \(2.3343\) | |
273273.f2 | 273273f1 | \([1, 1, 1, 113987, 12242810]\) | \(98931640625/96059601\) | \(-159035841898620687\) | \([2]\) | \(2764800\) | \(1.9877\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 273273.f have rank \(1\).
Complex multiplication
The elliptic curves in class 273273.f do not have complex multiplication.Modular form 273273.2.a.f
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.