Show commands:
SageMath
E = EllipticCurve("df1")
E.isogeny_class()
Elliptic curves in class 54096.df
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 54096.df1 | 54096di2 | \([0, 1, 0, -21184, -5423692]\) | \(-2181825073/25039686\) | \(-12066381898604544\) | \([]\) | \(414720\) | \(1.7677\) | |
| 54096.df2 | 54096di1 | \([0, 1, 0, 2336, 192884]\) | \(2924207/34776\) | \(-16758217211904\) | \([]\) | \(138240\) | \(1.2184\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 54096.df have rank \(1\).
Complex multiplication
The elliptic curves in class 54096.df do not have complex multiplication.Modular form 54096.2.a.df
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.
