Show commands:
SageMath
E = EllipticCurve("dj1")
E.isogeny_class()
Elliptic curves in class 338130.dj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
338130.dj1 | 338130dj2 | \([1, -1, 1, -191687, 29226111]\) | \(217482980991353/23168683200\) | \(82980422869406400\) | \([2]\) | \(5603328\) | \(1.9809\) | |
338130.dj2 | 338130dj1 | \([1, -1, 1, -44807, -3146241]\) | \(2777652643193/404951040\) | \(1450363330990080\) | \([2]\) | \(2801664\) | \(1.6343\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 338130.dj have rank \(1\).
Complex multiplication
The elliptic curves in class 338130.dj do not have complex multiplication.Modular form 338130.2.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 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.