Show commands:
SageMath
E = EllipticCurve("dl1")
E.isogeny_class()
Elliptic curves in class 72450.dl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 72450.dl1 | 72450cv2 | \([1, -1, 1, -47104055, 124444770447]\) | \(219181950070420668759/1154048\) | \(60858000000000\) | \([2]\) | \(4608000\) | \(2.7194\) | |
| 72450.dl2 | 72450cv1 | \([1, -1, 1, -2944055, 1944930447]\) | \(53514014005477719/3882876928\) | \(204761088000000000\) | \([2]\) | \(2304000\) | \(2.3729\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 72450.dl have rank \(1\).
Complex multiplication
The elliptic curves in class 72450.dl do not have complex multiplication.Modular form 72450.2.a.dl
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
