Show commands:
SageMath
E = EllipticCurve("hx1")
E.isogeny_class()
Elliptic curves in class 148800hx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 148800.jk2 | 148800hx1 | \([0, 1, 0, 3967, -1403937]\) | \(1685159/209250\) | \(-857088000000000\) | \([]\) | \(552960\) | \(1.5447\) | \(\Gamma_0(N)\)-optimal |
| 148800.jk1 | 148800hx2 | \([0, 1, 0, -836033, -294563937]\) | \(-15777367606441/3574920\) | \(-14642872320000000\) | \([]\) | \(1658880\) | \(2.0940\) |
Rank
sage: E.rank()
The elliptic curves in class 148800hx have rank \(1\).
Complex multiplication
The elliptic curves in class 148800hx do not have complex multiplication.Modular form 148800.2.a.hx
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.
