Show commands for:
SageMath
sage: E = EllipticCurve("df1")
sage: E.isogeny_class()
Elliptic curves in class 443760.df
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
443760.df1 | 443760df3 | [0, 1, 0, -24806800, 47223347348] | [2] | 34062336 | \(\Gamma_0(N)\)-optimal* |
443760.df2 | 443760df2 | [0, 1, 0, -2618800, -409851052] | [2, 2] | 17031168 | \(\Gamma_0(N)\)-optimal* |
443760.df3 | 443760df1 | [0, 1, 0, -2027120, -1110163500] | [2] | 8515584 | \(\Gamma_0(N)\)-optimal* |
443760.df4 | 443760df4 | [0, 1, 0, 10102320, -3213585900] | [4] | 34062336 |
Rank
sage: E.rank()
The elliptic curves in class 443760.df have rank \(1\).
Complex multiplication
The elliptic curves in class 443760.df do not have complex multiplication.Modular form 443760.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.