Show commands:
SageMath
E = EllipticCurve("fh1")
E.isogeny_class()
Elliptic curves in class 458640fh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 458640.fh1 | 458640fh1 | \([0, 0, 0, -32928, 2310448]\) | \(-303464448/1625\) | \(-21142937088000\) | \([]\) | \(1306368\) | \(1.4014\) | \(\Gamma_0(N)\)-optimal |
| 458640.fh2 | 458640fh2 | \([0, 0, 0, 84672, 12298608]\) | \(7077888/10985\) | \(-104193239687147520\) | \([]\) | \(3919104\) | \(1.9507\) |
Rank
sage: E.rank()
The elliptic curves in class 458640fh have rank \(1\).
Complex multiplication
The elliptic curves in class 458640fh do not have complex multiplication.Modular form 458640.2.a.fh
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
