Show commands:
SageMath
E = EllipticCurve("fi1")
E.isogeny_class()
Elliptic curves in class 202800.fi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
202800.fi1 | 202800kl1 | \([0, -1, 0, -14083, 299662]\) | \(256000/117\) | \(141184163250000\) | \([2]\) | \(774144\) | \(1.4100\) | \(\Gamma_0(N)\)-optimal |
202800.fi2 | 202800kl2 | \([0, -1, 0, 49292, 2200912]\) | \(686000/507\) | \(-9788768652000000\) | \([2]\) | \(1548288\) | \(1.7566\) |
Rank
sage: E.rank()
The elliptic curves in class 202800.fi have rank \(1\).
Complex multiplication
The elliptic curves in class 202800.fi do not have complex multiplication.Modular form 202800.2.a.fi
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.