Show commands:
SageMath
E = EllipticCurve("dj1")
E.isogeny_class()
Elliptic curves in class 426888dj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
426888.dj2 | 426888dj1 | \([0, 0, 0, -88935, 8217594]\) | \(54000/11\) | \(15846770402926848\) | \([2]\) | \(2764800\) | \(1.8241\) | \(\Gamma_0(N)\)-optimal |
426888.dj1 | 426888dj2 | \([0, 0, 0, -444675, -106828722]\) | \(1687500/121\) | \(697257897728781312\) | \([2]\) | \(5529600\) | \(2.1707\) |
Rank
sage: E.rank()
The elliptic curves in class 426888dj have rank \(1\).
Complex multiplication
The elliptic curves in class 426888dj do not have complex multiplication.Modular form 426888.2.a.dj
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.