Show commands:
SageMath
E = EllipticCurve("cz1")
E.isogeny_class()
Elliptic curves in class 22050.cz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 22050.cz1 | 22050fu2 | \([1, -1, 1, -154580, -24711753]\) | \(-7620530425/526848\) | \(-28241068322880000\) | \([]\) | \(248832\) | \(1.9076\) | |
| 22050.cz2 | 22050fu1 | \([1, -1, 1, 10795, -37803]\) | \(2595575/1512\) | \(-81048984345000\) | \([]\) | \(82944\) | \(1.3583\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 22050.cz have rank \(1\).
Complex multiplication
The elliptic curves in class 22050.cz do not have complex multiplication.Modular form 22050.2.a.cz
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
