Show commands:
SageMath
E = EllipticCurve("hf1")
E.isogeny_class()
Elliptic curves in class 88200.hf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 88200.hf1 | 88200fh2 | \([0, 0, 0, -15435, -737450]\) | \(1000188\) | \(406594944000\) | \([2]\) | \(147456\) | \(1.1470\) | |
| 88200.hf2 | 88200fh1 | \([0, 0, 0, -735, -17150]\) | \(-432\) | \(-101648736000\) | \([2]\) | \(73728\) | \(0.80045\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 88200.hf have rank \(0\).
Complex multiplication
The elliptic curves in class 88200.hf do not have complex multiplication.Modular form 88200.2.a.hf
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.
