Show commands:
SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 139650.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
139650.x1 | 139650ix2 | \([1, 1, 0, -222100, 39346000]\) | \(226077997131559/5457072384\) | \(29246497308000000\) | \([2]\) | \(1310720\) | \(1.9440\) | |
139650.x2 | 139650ix1 | \([1, 1, 0, 1900, 1938000]\) | \(141420761/302579712\) | \(-1621638144000000\) | \([2]\) | \(655360\) | \(1.5975\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 139650.x have rank \(1\).
Complex multiplication
The elliptic curves in class 139650.x do not have complex multiplication.Modular form 139650.2.a.x
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.